NO Initial ITS Start location: l7 Program variables: result_4^0 tmp_7^0 x_5^0 y_6^0 0: l0 -> l1 : result_4^0'=result_4^post1, tmp_7^0'=tmp_7^post1, x_5^0'=x_5^post1, y_6^0'=y_6^post1, (0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ -y_6^post1+y_6^0 == 0 /\ -x_5^0+y_6^0 <= 0 /\ tmp_7^0-tmp_7^post1 == 0), cost: 1 1: l0 -> l2 : result_4^0'=result_4^post2, tmp_7^0'=tmp_7^post2, x_5^0'=x_5^post2, y_6^0'=y_6^post2, (0 == 0 /\ tmp_7^post2 <= 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -tmp_7^post2 <= 0 /\ -1+y_6^post2-y_6^0 == 0 /\ -result_4^post2+result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 3: l0 -> l4 : result_4^0'=result_4^post4, tmp_7^0'=tmp_7^post4, x_5^0'=x_5^post4, y_6^0'=y_6^post4, (0 == 0 /\ x_5^0-x_5^post4 == 0 /\ -y_6^post4+y_6^0 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -result_4^post4+result_4^0 == 0), cost: 1 2: l2 -> l0 : result_4^0'=result_4^post3, tmp_7^0'=tmp_7^post3, x_5^0'=x_5^post3, y_6^0'=y_6^post3, (-y_6^post3+y_6^0 == 0 /\ -tmp_7^post3+tmp_7^0 == 0 /\ -result_4^post3+result_4^0 == 0 /\ -x_5^post3+x_5^0 == 0), cost: 1 4: l4 -> l5 : result_4^0'=result_4^post5, tmp_7^0'=tmp_7^post5, x_5^0'=x_5^post5, y_6^0'=y_6^post5, (-y_6^post5+y_6^0 == 0 /\ -result_4^post5+result_4^0 == 0 /\ tmp_7^0-tmp_7^post5 == 0 /\ -x_5^post5+x_5^0 == 0 /\ 1+tmp_7^0 <= 0), cost: 1 5: l4 -> l5 : result_4^0'=result_4^post6, tmp_7^0'=tmp_7^post6, x_5^0'=x_5^post6, y_6^0'=y_6^post6, (-result_4^post6+result_4^0 == 0 /\ 1-tmp_7^0 <= 0 /\ -x_5^post6+x_5^0 == 0 /\ tmp_7^0-tmp_7^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1 6: l5 -> l3 : result_4^0'=result_4^post7, tmp_7^0'=tmp_7^post7, x_5^0'=x_5^post7, y_6^0'=y_6^post7, (-1+x_5^post7-x_5^0 == 0 /\ result_4^0-result_4^post7 == 0 /\ -tmp_7^post7+tmp_7^0 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 7: l3 -> l0 : result_4^0'=result_4^post8, tmp_7^0'=tmp_7^post8, x_5^0'=x_5^post8, y_6^0'=y_6^post8, (x_5^0-x_5^post8 == 0 /\ -tmp_7^post8+tmp_7^0 == 0 /\ -result_4^post8+result_4^0 == 0 /\ -y_6^post8+y_6^0 == 0), cost: 1 8: l6 -> l0 : result_4^0'=result_4^post9, tmp_7^0'=tmp_7^post9, x_5^0'=x_5^post9, y_6^0'=y_6^post9, (x_5^0-x_5^post9 == 0 /\ tmp_7^0-tmp_7^post9 == 0 /\ -y_6^post9+y_6^0 == 0 /\ -result_4^post9+result_4^0 == 0), cost: 1 9: l7 -> l6 : result_4^0'=result_4^post10, tmp_7^0'=tmp_7^post10, x_5^0'=x_5^post10, y_6^0'=y_6^post10, (-x_5^post10+x_5^0 == 0 /\ -result_4^post10+result_4^0 == 0 /\ -y_6^post10+y_6^0 == 0 /\ tmp_7^0-tmp_7^post10 == 0), cost: 1 Chained Linear Paths Start location: l7 Program variables: result_4^0 tmp_7^0 x_5^0 y_6^0 0: l0 -> l1 : result_4^0'=result_4^post1, tmp_7^0'=tmp_7^post1, x_5^0'=x_5^post1, y_6^0'=y_6^post1, (0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ -y_6^post1+y_6^0 == 0 /\ -x_5^0+y_6^0 <= 0 /\ tmp_7^0-tmp_7^post1 == 0), cost: 1 3: l0 -> l4 : result_4^0'=result_4^post4, tmp_7^0'=tmp_7^post4, x_5^0'=x_5^post4, y_6^0'=y_6^post4, (0 == 0 /\ x_5^0-x_5^post4 == 0 /\ -y_6^post4+y_6^0 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -result_4^post4+result_4^0 == 0), cost: 1 11: l0 -> l0 : result_4^0'=result_4^post3, tmp_7^0'=tmp_7^post3, x_5^0'=x_5^post3, y_6^0'=y_6^post3, (0 == 0 /\ tmp_7^post2 <= 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -tmp_7^post2 <= 0 /\ y_6^post2-y_6^post3 == 0 /\ x_5^post2-x_5^post3 == 0 /\ -result_4^post3+result_4^post2 == 0 /\ -1+y_6^post2-y_6^0 == 0 /\ tmp_7^post2-tmp_7^post3 == 0 /\ -result_4^post2+result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 4: l4 -> l5 : result_4^0'=result_4^post5, tmp_7^0'=tmp_7^post5, x_5^0'=x_5^post5, y_6^0'=y_6^post5, (-y_6^post5+y_6^0 == 0 /\ -result_4^post5+result_4^0 == 0 /\ tmp_7^0-tmp_7^post5 == 0 /\ -x_5^post5+x_5^0 == 0 /\ 1+tmp_7^0 <= 0), cost: 1 5: l4 -> l5 : result_4^0'=result_4^post6, tmp_7^0'=tmp_7^post6, x_5^0'=x_5^post6, y_6^0'=y_6^post6, (-result_4^post6+result_4^0 == 0 /\ 1-tmp_7^0 <= 0 /\ -x_5^post6+x_5^0 == 0 /\ tmp_7^0-tmp_7^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1 12: l5 -> l0 : result_4^0'=result_4^post8, tmp_7^0'=tmp_7^post8, x_5^0'=x_5^post8, y_6^0'=y_6^post8, (tmp_7^post7-tmp_7^post8 == 0 /\ -1+x_5^post7-x_5^0 == 0 /\ result_4^0-result_4^post7 == 0 /\ -y_6^post8+y_6^post7 == 0 /\ -tmp_7^post7+tmp_7^0 == 0 /\ x_5^post7-x_5^post8 == 0 /\ -result_4^post8+result_4^post7 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 10: l7 -> l0 : result_4^0'=result_4^post9, tmp_7^0'=tmp_7^post9, x_5^0'=x_5^post9, y_6^0'=y_6^post9, (-y_6^post9+y_6^post10 == 0 /\ -result_4^post9+result_4^post10 == 0 /\ -tmp_7^post9+tmp_7^post10 == 0 /\ -x_5^post10+x_5^0 == 0 /\ -result_4^post10+result_4^0 == 0 /\ -y_6^post10+y_6^0 == 0 /\ x_5^post10-x_5^post9 == 0 /\ tmp_7^0-tmp_7^post10 == 0), cost: 1 Eliminating location l6 by chaining: Applied chaining First rule: l7 -> l6 : result_4^0'=result_4^post10, tmp_7^0'=tmp_7^post10, x_5^0'=x_5^post10, y_6^0'=y_6^post10, (-x_5^post10+x_5^0 == 0 /\ -result_4^post10+result_4^0 == 0 /\ -y_6^post10+y_6^0 == 0 /\ tmp_7^0-tmp_7^post10 == 0), cost: 1 Second rule: l6 -> l0 : result_4^0'=result_4^post9, tmp_7^0'=tmp_7^post9, x_5^0'=x_5^post9, y_6^0'=y_6^post9, (x_5^0-x_5^post9 == 0 /\ tmp_7^0-tmp_7^post9 == 0 /\ -y_6^post9+y_6^0 == 0 /\ -result_4^post9+result_4^0 == 0), cost: 1 New rule: l7 -> l0 : result_4^0'=result_4^post9, tmp_7^0'=tmp_7^post9, x_5^0'=x_5^post9, y_6^0'=y_6^post9, (-y_6^post9+y_6^post10 == 0 /\ -result_4^post9+result_4^post10 == 0 /\ -tmp_7^post9+tmp_7^post10 == 0 /\ -x_5^post10+x_5^0 == 0 /\ -result_4^post10+result_4^0 == 0 /\ -y_6^post10+y_6^0 == 0 /\ x_5^post10-x_5^post9 == 0 /\ tmp_7^0-tmp_7^post10 == 0), cost: 1 Applied deletion Removed the following rules: 8 9 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : result_4^0'=result_4^post2, tmp_7^0'=tmp_7^post2, x_5^0'=x_5^post2, y_6^0'=y_6^post2, (0 == 0 /\ tmp_7^post2 <= 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -tmp_7^post2 <= 0 /\ -1+y_6^post2-y_6^0 == 0 /\ -result_4^post2+result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 Second rule: l2 -> l0 : result_4^0'=result_4^post3, tmp_7^0'=tmp_7^post3, x_5^0'=x_5^post3, y_6^0'=y_6^post3, (-y_6^post3+y_6^0 == 0 /\ -tmp_7^post3+tmp_7^0 == 0 /\ -result_4^post3+result_4^0 == 0 /\ -x_5^post3+x_5^0 == 0), cost: 1 New rule: l0 -> l0 : result_4^0'=result_4^post3, tmp_7^0'=tmp_7^post3, x_5^0'=x_5^post3, y_6^0'=y_6^post3, (0 == 0 /\ tmp_7^post2 <= 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -tmp_7^post2 <= 0 /\ y_6^post2-y_6^post3 == 0 /\ x_5^post2-x_5^post3 == 0 /\ -result_4^post3+result_4^post2 == 0 /\ -1+y_6^post2-y_6^0 == 0 /\ tmp_7^post2-tmp_7^post3 == 0 /\ -result_4^post2+result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 Applied deletion Removed the following rules: 1 2 Eliminating location l3 by chaining: Applied chaining First rule: l5 -> l3 : result_4^0'=result_4^post7, tmp_7^0'=tmp_7^post7, x_5^0'=x_5^post7, y_6^0'=y_6^post7, (-1+x_5^post7-x_5^0 == 0 /\ result_4^0-result_4^post7 == 0 /\ -tmp_7^post7+tmp_7^0 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 Second rule: l3 -> l0 : result_4^0'=result_4^post8, tmp_7^0'=tmp_7^post8, x_5^0'=x_5^post8, y_6^0'=y_6^post8, (x_5^0-x_5^post8 == 0 /\ -tmp_7^post8+tmp_7^0 == 0 /\ -result_4^post8+result_4^0 == 0 /\ -y_6^post8+y_6^0 == 0), cost: 1 New rule: l5 -> l0 : result_4^0'=result_4^post8, tmp_7^0'=tmp_7^post8, x_5^0'=x_5^post8, y_6^0'=y_6^post8, (tmp_7^post7-tmp_7^post8 == 0 /\ -1+x_5^post7-x_5^0 == 0 /\ result_4^0-result_4^post7 == 0 /\ -y_6^post8+y_6^post7 == 0 /\ -tmp_7^post7+tmp_7^0 == 0 /\ x_5^post7-x_5^post8 == 0 /\ -result_4^post8+result_4^post7 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 Applied deletion Removed the following rules: 6 7 Simplified Transitions Start location: l7 Program variables: result_4^0 tmp_7^0 x_5^0 y_6^0 13: l0 -> l1 : result_4^0'=result_4^post1, -x_5^0+y_6^0 <= 0, cost: 1 14: l0 -> l4 : tmp_7^0'=tmp_7^post4, 1+x_5^0-y_6^0 <= 0, cost: 1 18: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 15: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 16: l4 -> l5 : 1-tmp_7^0 <= 0, cost: 1 19: l5 -> l0 : x_5^0'=1+x_5^0, T, cost: 1 17: l7 -> l0 : T, cost: 1 Propagated Equalities Original rule: l0 -> l1 : result_4^0'=result_4^post1, tmp_7^0'=tmp_7^post1, x_5^0'=x_5^post1, y_6^0'=y_6^post1, (0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ -y_6^post1+y_6^0 == 0 /\ -x_5^0+y_6^0 <= 0 /\ tmp_7^0-tmp_7^post1 == 0), cost: 1 New rule: l0 -> l1 : result_4^0'=result_4^post1, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, (0 == 0 /\ -x_5^0+y_6^0 <= 0), cost: 1 propagated equality x_5^post1 = x_5^0 propagated equality y_6^post1 = y_6^0 propagated equality tmp_7^post1 = tmp_7^0 Simplified Guard Original rule: l0 -> l1 : result_4^0'=result_4^post1, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, (0 == 0 /\ -x_5^0+y_6^0 <= 0), cost: 1 New rule: l0 -> l1 : result_4^0'=result_4^post1, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, -x_5^0+y_6^0 <= 0, cost: 1 Removed Trivial Updates Original rule: l0 -> l1 : result_4^0'=result_4^post1, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, -x_5^0+y_6^0 <= 0, cost: 1 New rule: l0 -> l1 : result_4^0'=result_4^post1, -x_5^0+y_6^0 <= 0, cost: 1 Propagated Equalities Original rule: l0 -> l4 : result_4^0'=result_4^post4, tmp_7^0'=tmp_7^post4, x_5^0'=x_5^post4, y_6^0'=y_6^post4, (0 == 0 /\ x_5^0-x_5^post4 == 0 /\ -y_6^post4+y_6^0 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -result_4^post4+result_4^0 == 0), cost: 1 New rule: l0 -> l4 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^post4, x_5^0'=x_5^0, y_6^0'=y_6^0, (0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 propagated equality x_5^post4 = x_5^0 propagated equality y_6^post4 = y_6^0 propagated equality result_4^post4 = result_4^0 Simplified Guard Original rule: l0 -> l4 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^post4, x_5^0'=x_5^0, y_6^0'=y_6^0, (0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 New rule: l0 -> l4 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^post4, x_5^0'=x_5^0, y_6^0'=y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 Removed Trivial Updates Original rule: l0 -> l4 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^post4, x_5^0'=x_5^0, y_6^0'=y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 New rule: l0 -> l4 : tmp_7^0'=tmp_7^post4, 1+x_5^0-y_6^0 <= 0, cost: 1 Propagated Equalities Original rule: l4 -> l5 : result_4^0'=result_4^post5, tmp_7^0'=tmp_7^post5, x_5^0'=x_5^post5, y_6^0'=y_6^post5, (-y_6^post5+y_6^0 == 0 /\ -result_4^post5+result_4^0 == 0 /\ tmp_7^0-tmp_7^post5 == 0 /\ -x_5^post5+x_5^0 == 0 /\ 1+tmp_7^0 <= 0), cost: 1 New rule: l4 -> l5 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, (0 == 0 /\ 1+tmp_7^0 <= 0), cost: 1 propagated equality y_6^post5 = y_6^0 propagated equality result_4^post5 = result_4^0 propagated equality tmp_7^post5 = tmp_7^0 propagated equality x_5^post5 = x_5^0 Simplified Guard Original rule: l4 -> l5 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, (0 == 0 /\ 1+tmp_7^0 <= 0), cost: 1 New rule: l4 -> l5 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, 1+tmp_7^0 <= 0, cost: 1 Removed Trivial Updates Original rule: l4 -> l5 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, 1+tmp_7^0 <= 0, cost: 1 New rule: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 Propagated Equalities Original rule: l4 -> l5 : result_4^0'=result_4^post6, tmp_7^0'=tmp_7^post6, x_5^0'=x_5^post6, y_6^0'=y_6^post6, (-result_4^post6+result_4^0 == 0 /\ 1-tmp_7^0 <= 0 /\ -x_5^post6+x_5^0 == 0 /\ tmp_7^0-tmp_7^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1 New rule: l4 -> l5 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, (0 == 0 /\ 1-tmp_7^0 <= 0), cost: 1 propagated equality result_4^post6 = result_4^0 propagated equality x_5^post6 = x_5^0 propagated equality tmp_7^post6 = tmp_7^0 propagated equality y_6^post6 = y_6^0 Simplified Guard Original rule: l4 -> l5 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, (0 == 0 /\ 1-tmp_7^0 <= 0), cost: 1 New rule: l4 -> l5 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, 1-tmp_7^0 <= 0, cost: 1 Removed Trivial Updates Original rule: l4 -> l5 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, 1-tmp_7^0 <= 0, cost: 1 New rule: l4 -> l5 : 1-tmp_7^0 <= 0, cost: 1 Propagated Equalities Original rule: l7 -> l0 : result_4^0'=result_4^post9, tmp_7^0'=tmp_7^post9, x_5^0'=x_5^post9, y_6^0'=y_6^post9, (-y_6^post9+y_6^post10 == 0 /\ -result_4^post9+result_4^post10 == 0 /\ -tmp_7^post9+tmp_7^post10 == 0 /\ -x_5^post10+x_5^0 == 0 /\ -result_4^post10+result_4^0 == 0 /\ -y_6^post10+y_6^0 == 0 /\ x_5^post10-x_5^post9 == 0 /\ tmp_7^0-tmp_7^post10 == 0), cost: 1 New rule: l7 -> l0 : result_4^0'=result_4^post10, tmp_7^0'=tmp_7^post10, x_5^0'=x_5^post10, y_6^0'=y_6^post10, (0 == 0 /\ -x_5^post10+x_5^0 == 0 /\ -result_4^post10+result_4^0 == 0 /\ -y_6^post10+y_6^0 == 0 /\ tmp_7^0-tmp_7^post10 == 0), cost: 1 propagated equality y_6^post9 = y_6^post10 propagated equality result_4^post9 = result_4^post10 propagated equality tmp_7^post9 = tmp_7^post10 propagated equality x_5^post9 = x_5^post10 Propagated Equalities Original rule: l7 -> l0 : result_4^0'=result_4^post10, tmp_7^0'=tmp_7^post10, x_5^0'=x_5^post10, y_6^0'=y_6^post10, (0 == 0 /\ -x_5^post10+x_5^0 == 0 /\ -result_4^post10+result_4^0 == 0 /\ -y_6^post10+y_6^0 == 0 /\ tmp_7^0-tmp_7^post10 == 0), cost: 1 New rule: l7 -> l0 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, 0 == 0, cost: 1 propagated equality x_5^post10 = x_5^0 propagated equality result_4^post10 = result_4^0 propagated equality y_6^post10 = y_6^0 propagated equality tmp_7^post10 = tmp_7^0 Simplified Guard Original rule: l7 -> l0 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, 0 == 0, cost: 1 New rule: l7 -> l0 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, T, cost: 1 Removed Trivial Updates Original rule: l7 -> l0 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=x_5^0, y_6^0'=y_6^0, T, cost: 1 New rule: l7 -> l0 : T, cost: 1 made implied equalities explicit Original rule: l0 -> l0 : result_4^0'=result_4^post3, tmp_7^0'=tmp_7^post3, x_5^0'=x_5^post3, y_6^0'=y_6^post3, (0 == 0 /\ tmp_7^post2 <= 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -tmp_7^post2 <= 0 /\ y_6^post2-y_6^post3 == 0 /\ x_5^post2-x_5^post3 == 0 /\ -result_4^post3+result_4^post2 == 0 /\ -1+y_6^post2-y_6^0 == 0 /\ tmp_7^post2-tmp_7^post3 == 0 /\ -result_4^post2+result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 New rule: l0 -> l0 : result_4^0'=result_4^post3, tmp_7^0'=tmp_7^post3, x_5^0'=x_5^post3, y_6^0'=y_6^post3, (0 == 0 /\ tmp_7^post2 <= 0 /\ tmp_7^post2 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -tmp_7^post2 <= 0 /\ y_6^post2-y_6^post3 == 0 /\ x_5^post2-x_5^post3 == 0 /\ -result_4^post3+result_4^post2 == 0 /\ -1+y_6^post2-y_6^0 == 0 /\ tmp_7^post2-tmp_7^post3 == 0 /\ -result_4^post2+result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 Propagated Equalities Original rule: l0 -> l0 : result_4^0'=result_4^post3, tmp_7^0'=tmp_7^post3, x_5^0'=x_5^post3, y_6^0'=y_6^post3, (0 == 0 /\ tmp_7^post2 <= 0 /\ tmp_7^post2 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -tmp_7^post2 <= 0 /\ y_6^post2-y_6^post3 == 0 /\ x_5^post2-x_5^post3 == 0 /\ -result_4^post3+result_4^post2 == 0 /\ -1+y_6^post2-y_6^0 == 0 /\ tmp_7^post2-tmp_7^post3 == 0 /\ -result_4^post2+result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 New rule: l0 -> l0 : result_4^0'=result_4^post2, tmp_7^0'=tmp_7^post2, x_5^0'=x_5^post2, y_6^0'=y_6^post2, (0 == 0 /\ tmp_7^post2 <= 0 /\ tmp_7^post2 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -tmp_7^post2 <= 0 /\ -1+y_6^post2-y_6^0 == 0 /\ -result_4^post2+result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 propagated equality y_6^post3 = y_6^post2 propagated equality x_5^post3 = x_5^post2 propagated equality result_4^post3 = result_4^post2 propagated equality tmp_7^post3 = tmp_7^post2 Propagated Equalities Original rule: l0 -> l0 : result_4^0'=result_4^post2, tmp_7^0'=tmp_7^post2, x_5^0'=x_5^post2, y_6^0'=y_6^post2, (0 == 0 /\ tmp_7^post2 <= 0 /\ tmp_7^post2 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -tmp_7^post2 <= 0 /\ -1+y_6^post2-y_6^0 == 0 /\ -result_4^post2+result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 New rule: l0 -> l0 : result_4^0'=result_4^0, tmp_7^0'=0, x_5^0'=x_5^0, y_6^0'=1+y_6^0, (0 <= 0 /\ 0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 propagated equality tmp_7^post2 = 0 propagated equality y_6^post2 = 1+y_6^0 propagated equality result_4^post2 = result_4^0 propagated equality x_5^post2 = x_5^0 Simplified Guard Original rule: l0 -> l0 : result_4^0'=result_4^0, tmp_7^0'=0, x_5^0'=x_5^0, y_6^0'=1+y_6^0, (0 <= 0 /\ 0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 New rule: l0 -> l0 : result_4^0'=result_4^0, tmp_7^0'=0, x_5^0'=x_5^0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 Removed Trivial Updates Original rule: l0 -> l0 : result_4^0'=result_4^0, tmp_7^0'=0, x_5^0'=x_5^0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 Propagated Equalities Original rule: l5 -> l0 : result_4^0'=result_4^post8, tmp_7^0'=tmp_7^post8, x_5^0'=x_5^post8, y_6^0'=y_6^post8, (tmp_7^post7-tmp_7^post8 == 0 /\ -1+x_5^post7-x_5^0 == 0 /\ result_4^0-result_4^post7 == 0 /\ -y_6^post8+y_6^post7 == 0 /\ -tmp_7^post7+tmp_7^0 == 0 /\ x_5^post7-x_5^post8 == 0 /\ -result_4^post8+result_4^post7 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 New rule: l5 -> l0 : result_4^0'=result_4^post7, tmp_7^0'=tmp_7^post7, x_5^0'=x_5^post7, y_6^0'=y_6^post7, (0 == 0 /\ -1+x_5^post7-x_5^0 == 0 /\ result_4^0-result_4^post7 == 0 /\ -tmp_7^post7+tmp_7^0 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 propagated equality tmp_7^post8 = tmp_7^post7 propagated equality y_6^post8 = y_6^post7 propagated equality x_5^post8 = x_5^post7 propagated equality result_4^post8 = result_4^post7 Propagated Equalities Original rule: l5 -> l0 : result_4^0'=result_4^post7, tmp_7^0'=tmp_7^post7, x_5^0'=x_5^post7, y_6^0'=y_6^post7, (0 == 0 /\ -1+x_5^post7-x_5^0 == 0 /\ result_4^0-result_4^post7 == 0 /\ -tmp_7^post7+tmp_7^0 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 New rule: l5 -> l0 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=1+x_5^0, y_6^0'=y_6^0, 0 == 0, cost: 1 propagated equality x_5^post7 = 1+x_5^0 propagated equality result_4^post7 = result_4^0 propagated equality tmp_7^post7 = tmp_7^0 propagated equality y_6^post7 = y_6^0 Simplified Guard Original rule: l5 -> l0 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=1+x_5^0, y_6^0'=y_6^0, 0 == 0, cost: 1 New rule: l5 -> l0 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=1+x_5^0, y_6^0'=y_6^0, T, cost: 1 Removed Trivial Updates Original rule: l5 -> l0 : result_4^0'=result_4^0, tmp_7^0'=tmp_7^0, x_5^0'=1+x_5^0, y_6^0'=y_6^0, T, cost: 1 New rule: l5 -> l0 : x_5^0'=1+x_5^0, T, cost: 1 Step with 17 Trace 17[T] Blocked [{}, {}] Step with 13 Trace 17[T], 13[(-x_5^0+y_6^0 <= 0)] Blocked [{}, {}, {}] Backtrack Trace 17[T] Blocked [{}, {13[T]}] Step with 14 Trace 17[T], 14[(1+x_5^0-y_6^0 <= 0)] Blocked [{}, {13[T]}, {}] Step with 15 Trace 17[T], 14[(1+x_5^0-y_6^0 <= 0)], 15[(1+tmp_7^0 <= 0)] Blocked [{}, {13[T]}, {}, {}] Step with 19 Trace 17[T], 14[(1+x_5^0-y_6^0 <= 0)], 15[(1+tmp_7^0 <= 0)], 19[T] Blocked [{}, {13[T]}, {}, {}, {}] Accelerate Start location: l7 Program variables: result_4^0 tmp_7^0 x_5^0 y_6^0 13: l0 -> l1 : result_4^0'=result_4^post1, -x_5^0+y_6^0 <= 0, cost: 1 14: l0 -> l4 : tmp_7^0'=tmp_7^post4, 1+x_5^0-y_6^0 <= 0, cost: 1 18: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 20: l0 -> l0 : tmp_7^0'=tmp_7^post41, x_5^0'=n+x_5^0, (-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0), cost: 1 15: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 16: l4 -> l5 : 1-tmp_7^0 <= 0, cost: 1 19: l5 -> l0 : x_5^0'=1+x_5^0, T, cost: 1 17: l7 -> l0 : T, cost: 1 Loop Acceleration Original rule: l0 -> l0 : tmp_7^0'=tmp_7^post41, x_5^0'=1+x_5^0, (1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post41 <= 0), cost: 1 New rule: l0 -> l0 : tmp_7^0'=tmp_7^post41, x_5^0'=n+x_5^0, (-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0), cost: 1 -1-tmp_7^post41 >= 0 [0]: monotonic increase yields -1-tmp_7^post41 >= 0 -1-x_5^0+y_6^0 >= 0 [0]: montonic decrease yields -n-x_5^0+y_6^0 >= 0 -1-x_5^0+y_6^0 >= 0 [1]: eventual increase yields (1 <= 0 /\ -1-x_5^0+y_6^0 >= 0) Replacement map: {-1-tmp_7^post41 >= 0 -> -1-tmp_7^post41 >= 0, -1-x_5^0+y_6^0 >= 0 -> -n-x_5^0+y_6^0 >= 0} Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)] Blocked [{}, {13[T]}, {20[T]}] Step with 13 Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)], 13[(-x_5^0+y_6^0 <= 0)] Blocked [{}, {13[T]}, {20[T]}, {}] Backtrack Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)] Blocked [{}, {13[T]}, {13[T], 20[T]}] Step with 14 Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 20[T]}, {}] Step with 15 Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 15[(1+tmp_7^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 20[T]}, {}, {}] Step with 19 Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 15[(1+tmp_7^0 <= 0)], 19[T] Blocked [{}, {13[T]}, {13[T], 20[T]}, {}, {}, {}] Covered Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 15[(1+tmp_7^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 20[T]}, {}, {19[T]}] Backtrack Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 20[T]}, {15[T]}] Step with 16 Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 16[(1-tmp_7^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 20[T]}, {15[T]}, {}] Step with 19 Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 16[(1-tmp_7^0 <= 0)], 19[T] Blocked [{}, {13[T]}, {13[T], 20[T]}, {15[T]}, {}, {}] Accelerate Start location: l7 Program variables: result_4^0 tmp_7^0 x_5^0 y_6^0 13: l0 -> l1 : result_4^0'=result_4^post1, -x_5^0+y_6^0 <= 0, cost: 1 14: l0 -> l4 : tmp_7^0'=tmp_7^post4, 1+x_5^0-y_6^0 <= 0, cost: 1 18: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 20: l0 -> l0 : tmp_7^0'=tmp_7^post41, x_5^0'=n+x_5^0, (-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0), cost: 1 21: l0 -> l0 : tmp_7^0'=tmp_7^post42, x_5^0'=n2+x_5^0, (-1+n2 >= 0 /\ -1+tmp_7^post42 >= 0 /\ -n2-x_5^0+y_6^0 >= 0), cost: 1 15: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 16: l4 -> l5 : 1-tmp_7^0 <= 0, cost: 1 19: l5 -> l0 : x_5^0'=1+x_5^0, T, cost: 1 17: l7 -> l0 : T, cost: 1 Loop Acceleration Original rule: l0 -> l0 : tmp_7^0'=tmp_7^post42, x_5^0'=1+x_5^0, (1+x_5^0-y_6^0 <= 0 /\ 1-tmp_7^post42 <= 0), cost: 1 New rule: l0 -> l0 : tmp_7^0'=tmp_7^post42, x_5^0'=n2+x_5^0, (-1+n2 >= 0 /\ -1+tmp_7^post42 >= 0 /\ -n2-x_5^0+y_6^0 >= 0), cost: 1 -1-x_5^0+y_6^0 >= 0 [0]: montonic decrease yields -n2-x_5^0+y_6^0 >= 0 -1-x_5^0+y_6^0 >= 0 [1]: eventual increase yields (1 <= 0 /\ -1-x_5^0+y_6^0 >= 0) -1+tmp_7^post42 >= 0 [0]: monotonic increase yields -1+tmp_7^post42 >= 0 Replacement map: {-1-x_5^0+y_6^0 >= 0 -> -n2-x_5^0+y_6^0 >= 0, -1+tmp_7^post42 >= 0 -> -1+tmp_7^post42 >= 0} Trace 17[T], 20[(-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0)], 21[(-1+n2 >= 0 /\ -1+tmp_7^post42 >= 0 /\ -n2-x_5^0+y_6^0 >= 0)] Blocked [{}, {13[T]}, {13[T], 20[T]}, {21[T]}] Accelerate Start location: l7 Program variables: result_4^0 tmp_7^0 x_5^0 y_6^0 13: l0 -> l1 : result_4^0'=result_4^post1, -x_5^0+y_6^0 <= 0, cost: 1 14: l0 -> l4 : tmp_7^0'=tmp_7^post4, 1+x_5^0-y_6^0 <= 0, cost: 1 18: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 20: l0 -> l0 : tmp_7^0'=tmp_7^post41, x_5^0'=n+x_5^0, (-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0), cost: 1 21: l0 -> l0 : tmp_7^0'=tmp_7^post42, x_5^0'=n2+x_5^0, (-1+n2 >= 0 /\ -1+tmp_7^post42 >= 0 /\ -n2-x_5^0+y_6^0 >= 0), cost: 1 22: l0 -> l0 : tmp_7^0'=tmp_7^post42, x_5^0'=n2*n3+n1*n3+x_5^0, (-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0), cost: 1 15: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 16: l4 -> l5 : 1-tmp_7^0 <= 0, cost: 1 19: l5 -> l0 : x_5^0'=1+x_5^0, T, cost: 1 17: l7 -> l0 : T, cost: 1 Loop Acceleration Original rule: l0 -> l0 : tmp_7^0'=tmp_7^post42, x_5^0'=n1+n2+x_5^0, (-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+tmp_7^post42 >= 0 /\ -n1-n2-x_5^0+y_6^0 >= 0 /\ -n1-x_5^0+y_6^0 >= 0), cost: 1 New rule: l0 -> l0 : tmp_7^0'=tmp_7^post42, x_5^0'=n2*n3+n1*n3+x_5^0, (-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0), cost: 1 -1+n1 >= 0 [0]: monotonic increase yields -1+n1 >= 0 -1+n2 >= 0 [0]: monotonic increase yields -1+n2 >= 0 -1+tmp_7^post42 >= 0 [0]: monotonic increase yields -1+tmp_7^post42 >= 0 -n1-n2-x_5^0+y_6^0 >= 0 [0]: montonic decrease yields -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0, dependencies: -1+n1 >= 0 -1+n2 >= 0 -n1-n2-x_5^0+y_6^0 >= 0 [1]: eventual increase yields (n1+n2 <= 0 /\ -n1-n2-x_5^0+y_6^0 >= 0) -n1-x_5^0+y_6^0 >= 0 [0]: montonic decrease yields -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0, dependencies: -1+n1 >= 0 -1+n2 >= 0 -n1-x_5^0+y_6^0 >= 0 [1]: eventual increase yields (n1+n2 <= 0 /\ -n1-x_5^0+y_6^0 >= 0) Replacement map: {-1+n1 >= 0 -> -1+n1 >= 0, -1+n2 >= 0 -> -1+n2 >= 0, -1+tmp_7^post42 >= 0 -> -1+tmp_7^post42 >= 0, -n1-n2-x_5^0+y_6^0 >= 0 -> -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0, -n1-x_5^0+y_6^0 >= 0 -> -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0} Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)] Blocked [{}, {13[T]}, {22[T]}] Step with 13 Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 13[(-x_5^0+y_6^0 <= 0)] Blocked [{}, {13[T]}, {22[T]}, {}] Backtrack Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)] Blocked [{}, {13[T]}, {13[T], 22[T]}] Step with 14 Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 22[T]}, {}] Step with 16 Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 16[(1-tmp_7^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 22[T]}, {}, {}] Step with 19 Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 16[(1-tmp_7^0 <= 0)], 19[T] Blocked [{}, {13[T]}, {13[T], 22[T]}, {}, {}, {}] Covered Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 16[(1-tmp_7^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 22[T]}, {}, {19[T]}] Backtrack Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 22[T]}, {16[T]}] Step with 15 Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 15[(1+tmp_7^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 22[T]}, {16[T]}, {}] Step with 19 Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 15[(1+tmp_7^0 <= 0)], 19[T] Blocked [{}, {13[T]}, {13[T], 22[T]}, {16[T]}, {}, {}] Covered Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)], 15[(1+tmp_7^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 22[T]}, {16[T]}, {19[T]}] Backtrack Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 14[(1+x_5^0-y_6^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 22[T]}, {15[T], 16[T]}] Backtrack Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)] Blocked [{}, {13[T]}, {13[T], 14[T], 22[T]}] Step with 18 Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 18[(1+x_5^0-y_6^0 <= 0)] Blocked [{}, {13[T]}, {13[T], 14[T], 22[T]}, {}] Nonterm Start location: l7 Program variables: result_4^0 tmp_7^0 x_5^0 y_6^0 13: l0 -> l1 : result_4^0'=result_4^post1, -x_5^0+y_6^0 <= 0, cost: 1 14: l0 -> l4 : tmp_7^0'=tmp_7^post4, 1+x_5^0-y_6^0 <= 0, cost: 1 18: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 20: l0 -> l0 : tmp_7^0'=tmp_7^post41, x_5^0'=n+x_5^0, (-1-tmp_7^post41 >= 0 /\ -1+n >= 0 /\ -n-x_5^0+y_6^0 >= 0), cost: 1 21: l0 -> l0 : tmp_7^0'=tmp_7^post42, x_5^0'=n2+x_5^0, (-1+n2 >= 0 /\ -1+tmp_7^post42 >= 0 /\ -n2-x_5^0+y_6^0 >= 0), cost: 1 22: l0 -> l0 : tmp_7^0'=tmp_7^post42, x_5^0'=n2*n3+n1*n3+x_5^0, (-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0), cost: 1 23: l0 -> LoAT_sink : (-1-x_5^0+y_6^0 >= 0 /\ -1+n4 >= 0), cost: NONTERM 24: l0 -> l0 : tmp_7^0'=0, y_6^0'=n4+y_6^0, (-1-x_5^0+y_6^0 >= 0 /\ -1+n4 >= 0), cost: 1 15: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 16: l4 -> l5 : 1-tmp_7^0 <= 0, cost: 1 19: l5 -> l0 : x_5^0'=1+x_5^0, T, cost: 1 17: l7 -> l0 : T, cost: 1 Certificate of Non-Termination Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, (1+x_5^0-y_6^0 <= 0), cost: 1 New rule: l0 -> LoAT_sink : (-1-x_5^0+y_6^0 >= 0 /\ -1+n4 >= 0), cost: NONTERM -1-x_5^0+y_6^0 >= 0 [0]: monotonic increase yields -1-x_5^0+y_6^0 >= 0 Replacement map: {-1-x_5^0+y_6^0 >= 0 -> -1-x_5^0+y_6^0 >= 0} Loop Acceleration Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, (1+x_5^0-y_6^0 <= 0), cost: 1 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=n4+y_6^0, (-1-x_5^0+y_6^0 >= 0 /\ -1+n4 >= 0), cost: 1 -1-x_5^0+y_6^0 >= 0 [0]: monotonic increase yields -1-x_5^0+y_6^0 >= 0 Replacement map: {-1-x_5^0+y_6^0 >= 0 -> -1-x_5^0+y_6^0 >= 0} Step with 23 Trace 17[T], 22[(-1+n1 >= 0 /\ -1+n2 >= 0 /\ -1+n3 >= 0 /\ -n1-n2-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -n1-n1*(-1+n3)-x_5^0-n2*(-1+n3)+y_6^0 >= 0 /\ -1+tmp_7^post42 >= 0)], 23[(-1-x_5^0+y_6^0 >= 0 /\ -1+n4 >= 0)] Blocked [{}, {13[T]}, {13[T], 14[T], 22[T]}, {23[T]}] Refute Counterexample [ result_4^0=0 tmp_7^0=0 x_5^0=-1 y_6^0=2 ] 17 [ result_4^0=0 tmp_7^0=1 x_5^0=1 y_6^0=2 ] 22 [ result_4^0=0 tmp_7^0=0 x_5^0=-1 y_6^0=2 ] 23 NO Build SHA: a05f16bf13df659c382799650051f91bf6828c7b