NO Initial ITS Start location: l6 0: l0 -> l1 : tmp_7^0'=tmp_7^post0, y_6^0'=y_6^post0, Result_4^0'=Result_4^post0, x_5^0'=x_5^post0, (0 == 0 /\ y_6^0-y_6^post0 == 0 /\ tmp_7^0-tmp_7^post0 == 0 /\ x_5^0-x_5^post0 == 0 /\ y_6^0-x_5^0 <= 0), cost: 1 1: l0 -> l2 : tmp_7^0'=tmp_7^post1, y_6^0'=y_6^post1, Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, (0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -tmp_7^post1 <= 0 /\ tmp_7^post1 <= 0 /\ 1-y_6^0+x_5^0 <= 0 /\ -x_5^post1+x_5^0 == 0 /\ 1-y_6^0+y_6^post1 == 0), cost: 1 3: l0 -> l4 : tmp_7^0'=tmp_7^post3, y_6^0'=y_6^post3, Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, (0 == 0 /\ -Result_4^post3+Result_4^0 == 0 /\ -x_5^post3+x_5^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 1 2: l2 -> l0 : tmp_7^0'=tmp_7^post2, y_6^0'=y_6^post2, Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, (-y_6^post2+y_6^0 == 0 /\ tmp_7^0-tmp_7^post2 == 0 /\ -Result_4^post2+Result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 4: l4 -> l3 : tmp_7^0'=tmp_7^post4, y_6^0'=y_6^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, (-Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+x_5^0 == 0 /\ 1+tmp_7^0 <= 0 /\ -y_6^post4+y_6^0 == 0 /\ -tmp_7^post4+tmp_7^0 == 0), cost: 1 5: l4 -> l3 : tmp_7^0'=tmp_7^post5, y_6^0'=y_6^post5, Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, (y_6^0-y_6^post5 == 0 /\ x_5^0-x_5^post5 == 0 /\ 1-tmp_7^0 <= 0 /\ tmp_7^0-tmp_7^post5 == 0 /\ Result_4^0-Result_4^post5 == 0), cost: 1 6: l3 -> l0 : tmp_7^0'=tmp_7^post6, y_6^0'=y_6^post6, Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, (tmp_7^0-tmp_7^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ y_6^0-y_6^post6 == 0 /\ -x_5^post6+x_5^0 == 0), cost: 1 7: l5 -> l0 : tmp_7^0'=tmp_7^post7, y_6^0'=y_6^post7, Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, (-x_5^post7+x_5^0 == 0 /\ -Result_4^post7+Result_4^0 == 0 /\ -y_6^post7+y_6^0 == 0 /\ tmp_7^0-tmp_7^post7 == 0), cost: 1 8: l6 -> l5 : tmp_7^0'=tmp_7^post8, y_6^0'=y_6^post8, Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, (x_5^0-x_5^post8 == 0 /\ -Result_4^post8+Result_4^0 == 0 /\ -tmp_7^post8+tmp_7^0 == 0 /\ y_6^0-y_6^post8 == 0), cost: 1 Removed unreachable rules and leafs Start location: l6 1: l0 -> l2 : tmp_7^0'=tmp_7^post1, y_6^0'=y_6^post1, Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, (0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -tmp_7^post1 <= 0 /\ tmp_7^post1 <= 0 /\ 1-y_6^0+x_5^0 <= 0 /\ -x_5^post1+x_5^0 == 0 /\ 1-y_6^0+y_6^post1 == 0), cost: 1 3: l0 -> l4 : tmp_7^0'=tmp_7^post3, y_6^0'=y_6^post3, Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, (0 == 0 /\ -Result_4^post3+Result_4^0 == 0 /\ -x_5^post3+x_5^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 1 2: l2 -> l0 : tmp_7^0'=tmp_7^post2, y_6^0'=y_6^post2, Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, (-y_6^post2+y_6^0 == 0 /\ tmp_7^0-tmp_7^post2 == 0 /\ -Result_4^post2+Result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 4: l4 -> l3 : tmp_7^0'=tmp_7^post4, y_6^0'=y_6^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, (-Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+x_5^0 == 0 /\ 1+tmp_7^0 <= 0 /\ -y_6^post4+y_6^0 == 0 /\ -tmp_7^post4+tmp_7^0 == 0), cost: 1 5: l4 -> l3 : tmp_7^0'=tmp_7^post5, y_6^0'=y_6^post5, Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, (y_6^0-y_6^post5 == 0 /\ x_5^0-x_5^post5 == 0 /\ 1-tmp_7^0 <= 0 /\ tmp_7^0-tmp_7^post5 == 0 /\ Result_4^0-Result_4^post5 == 0), cost: 1 6: l3 -> l0 : tmp_7^0'=tmp_7^post6, y_6^0'=y_6^post6, Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, (tmp_7^0-tmp_7^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ y_6^0-y_6^post6 == 0 /\ -x_5^post6+x_5^0 == 0), cost: 1 7: l5 -> l0 : tmp_7^0'=tmp_7^post7, y_6^0'=y_6^post7, Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, (-x_5^post7+x_5^0 == 0 /\ -Result_4^post7+Result_4^0 == 0 /\ -y_6^post7+y_6^0 == 0 /\ tmp_7^0-tmp_7^post7 == 0), cost: 1 8: l6 -> l5 : tmp_7^0'=tmp_7^post8, y_6^0'=y_6^post8, Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, (x_5^0-x_5^post8 == 0 /\ -Result_4^post8+Result_4^0 == 0 /\ -tmp_7^post8+tmp_7^0 == 0 /\ y_6^0-y_6^post8 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : tmp_7^0'=tmp_7^post1, y_6^0'=y_6^post1, Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, (0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -tmp_7^post1 <= 0 /\ tmp_7^post1 <= 0 /\ 1-y_6^0+x_5^0 <= 0 /\ -x_5^post1+x_5^0 == 0 /\ 1-y_6^0+y_6^post1 == 0), cost: 1 New rule: l0 -> l2 : tmp_7^0'=0, y_6^0'=-1+y_6^0, 1-y_6^0+x_5^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l0 : tmp_7^0'=tmp_7^post2, y_6^0'=y_6^post2, Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, (-y_6^post2+y_6^0 == 0 /\ tmp_7^0-tmp_7^post2 == 0 /\ -Result_4^post2+Result_4^0 == 0 /\ -x_5^post2+x_5^0 == 0), cost: 1 New rule: l2 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l0 -> l4 : tmp_7^0'=tmp_7^post3, y_6^0'=y_6^post3, Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, (0 == 0 /\ -Result_4^post3+Result_4^0 == 0 /\ -x_5^post3+x_5^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 1 New rule: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 1 Applied preprocessing Original rule: l4 -> l3 : tmp_7^0'=tmp_7^post4, y_6^0'=y_6^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, (-Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+x_5^0 == 0 /\ 1+tmp_7^0 <= 0 /\ -y_6^post4+y_6^0 == 0 /\ -tmp_7^post4+tmp_7^0 == 0), cost: 1 New rule: l4 -> l3 : 1+tmp_7^0 <= 0, cost: 1 Applied preprocessing Original rule: l4 -> l3 : tmp_7^0'=tmp_7^post5, y_6^0'=y_6^post5, Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, (y_6^0-y_6^post5 == 0 /\ x_5^0-x_5^post5 == 0 /\ 1-tmp_7^0 <= 0 /\ tmp_7^0-tmp_7^post5 == 0 /\ Result_4^0-Result_4^post5 == 0), cost: 1 New rule: l4 -> l3 : -1+tmp_7^0 >= 0, cost: 1 Applied preprocessing Original rule: l3 -> l0 : tmp_7^0'=tmp_7^post6, y_6^0'=y_6^post6, Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, (tmp_7^0-tmp_7^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ y_6^0-y_6^post6 == 0 /\ -x_5^post6+x_5^0 == 0), cost: 1 New rule: l3 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l0 : tmp_7^0'=tmp_7^post7, y_6^0'=y_6^post7, Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, (-x_5^post7+x_5^0 == 0 /\ -Result_4^post7+Result_4^0 == 0 /\ -y_6^post7+y_6^0 == 0 /\ tmp_7^0-tmp_7^post7 == 0), cost: 1 New rule: l5 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l5 : tmp_7^0'=tmp_7^post8, y_6^0'=y_6^post8, Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, (x_5^0-x_5^post8 == 0 /\ -Result_4^post8+Result_4^0 == 0 /\ -tmp_7^post8+tmp_7^0 == 0 /\ y_6^0-y_6^post8 == 0), cost: 1 New rule: l6 -> l5 : TRUE, cost: 1 Simplified rules Start location: l6 9: l0 -> l2 : tmp_7^0'=0, y_6^0'=-1+y_6^0, 1-y_6^0+x_5^0 <= 0, cost: 1 11: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 1 10: l2 -> l0 : TRUE, cost: 1 12: l4 -> l3 : 1+tmp_7^0 <= 0, cost: 1 13: l4 -> l3 : -1+tmp_7^0 >= 0, cost: 1 14: l3 -> l0 : TRUE, cost: 1 15: l5 -> l0 : TRUE, cost: 1 16: l6 -> l5 : TRUE, cost: 1 Eliminating location l5 by chaining: Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l0 : TRUE, cost: 1 New rule: l6 -> l0 : TRUE, cost: 2 Applied deletion Removed the following rules: 15 16 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : tmp_7^0'=0, y_6^0'=-1+y_6^0, 1-y_6^0+x_5^0 <= 0, cost: 1 Second rule: l2 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=-1+y_6^0, 1-y_6^0+x_5^0 <= 0, cost: 2 Applied deletion Removed the following rules: 9 10 Eliminated locations on linear paths Start location: l6 11: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 1 18: l0 -> l0 : tmp_7^0'=0, y_6^0'=-1+y_6^0, 1-y_6^0+x_5^0 <= 0, cost: 2 12: l4 -> l3 : 1+tmp_7^0 <= 0, cost: 1 13: l4 -> l3 : -1+tmp_7^0 >= 0, cost: 1 14: l3 -> l0 : TRUE, cost: 1 17: l6 -> l0 : TRUE, cost: 2 Applied acceleration Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=-1+y_6^0, 1-y_6^0+x_5^0 <= 0, cost: 2 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=y_6^0-n, (-1+n >= 0 /\ y_6^0-n-x_5^0 >= 0), cost: 2*n Sub-proof via acceration calculus written to file:///tmp/tmpnam_nAHMcH.txt Applied instantiation Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=y_6^0-n, (-1+n >= 0 /\ y_6^0-n-x_5^0 >= 0), cost: 2*n New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (0 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: 2*y_6^0-2*x_5^0 Applied simplification Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (0 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: 2*y_6^0-2*x_5^0 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2*y_6^0-2*x_5^0 Applied deletion Removed the following rules: 18 Accelerated simple loops Start location: l6 11: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 1 20: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2*y_6^0-2*x_5^0 12: l4 -> l3 : 1+tmp_7^0 <= 0, cost: 1 13: l4 -> l3 : -1+tmp_7^0 >= 0, cost: 1 14: l3 -> l0 : TRUE, cost: 1 17: l6 -> l0 : TRUE, cost: 2 Applied chaining First rule: l3 -> l0 : TRUE, cost: 1 Second rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2*y_6^0-2*x_5^0 New rule: l3 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 1+2*y_6^0-2*x_5^0 Applied chaining First rule: l6 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2*y_6^0-2*x_5^0 New rule: l6 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2+2*y_6^0-2*x_5^0 Applied deletion Removed the following rules: 20 Chained accelerated rules with incoming rules Start location: l6 11: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 1 12: l4 -> l3 : 1+tmp_7^0 <= 0, cost: 1 13: l4 -> l3 : -1+tmp_7^0 >= 0, cost: 1 14: l3 -> l0 : TRUE, cost: 1 21: l3 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 1+2*y_6^0-2*x_5^0 17: l6 -> l0 : TRUE, cost: 2 22: l6 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2+2*y_6^0-2*x_5^0 Eliminating location l4 by chaining: Applied chaining First rule: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 1 Second rule: l4 -> l3 : 1+tmp_7^0 <= 0, cost: 1 New rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 Applied chaining First rule: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 1 Second rule: l4 -> l3 : -1+tmp_7^0 >= 0, cost: 1 New rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 Applied deletion Removed the following rules: 11 12 13 Eliminated locations on tree-shaped paths Start location: l6 23: l0 -> l3 : tmp_7^0'=tmp_7^post3, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 24: l0 -> l3 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 14: l3 -> l0 : TRUE, cost: 1 21: l3 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 1+2*y_6^0-2*x_5^0 17: l6 -> l0 : TRUE, cost: 2 22: l6 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2+2*y_6^0-2*x_5^0 Eliminating location l3 by chaining: Applied chaining First rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 Second rule: l3 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : tmp_7^0'=tmp_7^post3, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3 Applied chaining First rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 Second rule: l3 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 1+2*y_6^0-2*x_5^0 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (-1+y_6^0-x_5^0 >= 0 /\ 1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 Applied simplification Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (-1+y_6^0-x_5^0 >= 0 /\ 1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 Applied chaining First rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 Second rule: l3 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3 Applied chaining First rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 Second rule: l3 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 1+2*y_6^0-2*x_5^0 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (-1+tmp_7^post3 >= 0 /\ -1+y_6^0-x_5^0 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 Applied simplification Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (-1+tmp_7^post3 >= 0 /\ -1+y_6^0-x_5^0 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 Applied deletion Removed the following rules: 14 21 23 24 Eliminated locations on tree-shaped paths Start location: l6 25: l0 -> l0 : tmp_7^0'=tmp_7^post3, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3 26: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 27: l0 -> l0 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3 28: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 17: l6 -> l0 : TRUE, cost: 2 22: l6 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2+2*y_6^0-2*x_5^0 Applied simplification Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, 1-y_6^0+x_5^0 <= 0, cost: 3+2*y_6^0-2*x_5^0 Applied simplification Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3+2*y_6^0-2*x_5^0 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, 1-y_6^0+x_5^0 <= 0, cost: 3+2*y_6^0-2*x_5^0 Simplified simple loops Start location: l6 25: l0 -> l0 : tmp_7^0'=tmp_7^post3, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3 27: l0 -> l0 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3 29: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, 1-y_6^0+x_5^0 <= 0, cost: 3+2*y_6^0-2*x_5^0 17: l6 -> l0 : TRUE, cost: 2 22: l6 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2+2*y_6^0-2*x_5^0 Applied nonterm Original rule: l0 -> l0 : tmp_7^0'=tmp_7^post3, (1+tmp_7^post3 <= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3 New rule: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ -1-tmp_7^post3 >= 0 /\ -1+n0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_dICIbb.txt Applied nonterm Original rule: l0 -> l0 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 3 New rule: l0 -> [8] : (-1+n1 >= 0 /\ -1+tmp_7^post3 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_cLghpJ.txt Applied simplification Original rule: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ -1-tmp_7^post3 >= 0 /\ -1+n0 >= 0), cost: NONTERM New rule: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ 1+tmp_7^post3 <= 0 /\ -1+n0 >= 0), cost: NONTERM Applied deletion Removed the following rules: 25 27 Accelerated simple loops Start location: l6 29: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, 1-y_6^0+x_5^0 <= 0, cost: 3+2*y_6^0-2*x_5^0 31: l0 -> [8] : (-1+n1 >= 0 /\ -1+tmp_7^post3 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: NONTERM 32: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ 1+tmp_7^post3 <= 0 /\ -1+n0 >= 0), cost: NONTERM 17: l6 -> l0 : TRUE, cost: 2 22: l6 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2+2*y_6^0-2*x_5^0 Applied chaining First rule: l6 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, 1-y_6^0+x_5^0 <= 0, cost: 3+2*y_6^0-2*x_5^0 New rule: l6 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, 1-y_6^0+x_5^0 <= 0, cost: 5+2*y_6^0-2*x_5^0 Applied chaining First rule: l6 -> l0 : TRUE, cost: 2 Second rule: l0 -> [8] : (-1+n1 >= 0 /\ -1+tmp_7^post3 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: NONTERM New rule: l6 -> [8] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l6 -> l0 : TRUE, cost: 2 Second rule: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ 1+tmp_7^post3 <= 0 /\ -1+n0 >= 0), cost: NONTERM New rule: l6 -> [8] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM Applied deletion Removed the following rules: 29 31 32 Chained accelerated rules with incoming rules Start location: l6 17: l6 -> l0 : TRUE, cost: 2 22: l6 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, -1+y_6^0-x_5^0 >= 0, cost: 2+2*y_6^0-2*x_5^0 33: l6 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, 1-y_6^0+x_5^0 <= 0, cost: 5+2*y_6^0-2*x_5^0 34: l6 -> [8] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l6 34: l6 -> [8] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 34 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -1+y_6^0-x_5^0 >= 0