NO Initial ITS Start location: l5 0: l0 -> l1 : x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, y_6^0'=y_6^post0, (0 == 0 /\ y_6^0-y_6^post0 == 0 /\ x_5^0-y_6^0 <= 0 /\ -x_5^0+y_6^0 <= 0 /\ x_5^0-x_5^post0 == 0), cost: 1 1: l0 -> l2 : x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, (-1-x_5^0+x_5^post1 == 0 /\ y_6^0-y_6^post1 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -x_5^0+y_6^0 <= 0 /\ 1-x_5^0+y_6^0 <= 0), cost: 1 3: l0 -> l3 : x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, (-Result_4^post3+Result_4^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ -1+x_5^post3-x_5^0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 2: l2 -> l0 : x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, (y_6^0-y_6^post2 == 0 /\ x_5^0-x_5^post2 == 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 4: l3 -> l0 : x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, (-Result_4^post4+Result_4^0 == 0 /\ -y_6^post4+y_6^0 == 0 /\ -x_5^post4+x_5^0 == 0), cost: 1 5: l4 -> l0 : x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, (-Result_4^post5+Result_4^0 == 0 /\ -y_6^post5+y_6^0 == 0 /\ -x_5^post5+x_5^0 == 0), cost: 1 6: l5 -> l4 : x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, (-Result_4^post6+Result_4^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l5 1: l0 -> l2 : x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, (-1-x_5^0+x_5^post1 == 0 /\ y_6^0-y_6^post1 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -x_5^0+y_6^0 <= 0 /\ 1-x_5^0+y_6^0 <= 0), cost: 1 3: l0 -> l3 : x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, (-Result_4^post3+Result_4^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ -1+x_5^post3-x_5^0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 2: l2 -> l0 : x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, (y_6^0-y_6^post2 == 0 /\ x_5^0-x_5^post2 == 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 4: l3 -> l0 : x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, (-Result_4^post4+Result_4^0 == 0 /\ -y_6^post4+y_6^0 == 0 /\ -x_5^post4+x_5^0 == 0), cost: 1 5: l4 -> l0 : x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, (-Result_4^post5+Result_4^0 == 0 /\ -y_6^post5+y_6^0 == 0 /\ -x_5^post5+x_5^0 == 0), cost: 1 6: l5 -> l4 : x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, (-Result_4^post6+Result_4^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, (-1-x_5^0+x_5^post1 == 0 /\ y_6^0-y_6^post1 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -x_5^0+y_6^0 <= 0 /\ 1-x_5^0+y_6^0 <= 0), cost: 1 New rule: l0 -> l2 : x_5^0'=1+x_5^0, 1-x_5^0+y_6^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l0 : x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, (y_6^0-y_6^post2 == 0 /\ x_5^0-x_5^post2 == 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 New rule: l2 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l0 -> l3 : x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, (-Result_4^post3+Result_4^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ -1+x_5^post3-x_5^0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 New rule: l0 -> l3 : x_5^0'=1+x_5^0, 1+x_5^0-y_6^0 <= 0, cost: 1 Applied preprocessing Original rule: l3 -> l0 : x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, (-Result_4^post4+Result_4^0 == 0 /\ -y_6^post4+y_6^0 == 0 /\ -x_5^post4+x_5^0 == 0), cost: 1 New rule: l3 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l0 : x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, (-Result_4^post5+Result_4^0 == 0 /\ -y_6^post5+y_6^0 == 0 /\ -x_5^post5+x_5^0 == 0), cost: 1 New rule: l4 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l4 : x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, (-Result_4^post6+Result_4^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1 New rule: l5 -> l4 : TRUE, cost: 1 Simplified rules Start location: l5 7: l0 -> l2 : x_5^0'=1+x_5^0, 1-x_5^0+y_6^0 <= 0, cost: 1 9: l0 -> l3 : x_5^0'=1+x_5^0, 1+x_5^0-y_6^0 <= 0, cost: 1 8: l2 -> l0 : TRUE, cost: 1 10: l3 -> l0 : TRUE, cost: 1 11: l4 -> l0 : TRUE, cost: 1 12: l5 -> l4 : TRUE, cost: 1 Eliminating location l4 by chaining: Applied chaining First rule: l5 -> l4 : TRUE, cost: 1 Second rule: l4 -> l0 : TRUE, cost: 1 New rule: l5 -> l0 : TRUE, cost: 2 Applied deletion Removed the following rules: 11 12 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : x_5^0'=1+x_5^0, 1-x_5^0+y_6^0 <= 0, cost: 1 Second rule: l2 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : x_5^0'=1+x_5^0, 1-x_5^0+y_6^0 <= 0, cost: 2 Applied deletion Removed the following rules: 7 8 Eliminating location l3 by chaining: Applied chaining First rule: l0 -> l3 : x_5^0'=1+x_5^0, 1+x_5^0-y_6^0 <= 0, cost: 1 Second rule: l3 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : x_5^0'=1+x_5^0, 1+x_5^0-y_6^0 <= 0, cost: 2 Applied deletion Removed the following rules: 9 10 Eliminated locations on linear paths Start location: l5 14: l0 -> l0 : x_5^0'=1+x_5^0, 1-x_5^0+y_6^0 <= 0, cost: 2 15: l0 -> l0 : x_5^0'=1+x_5^0, 1+x_5^0-y_6^0 <= 0, cost: 2 13: l5 -> l0 : TRUE, cost: 2 Applied nonterm Original rule: l0 -> l0 : x_5^0'=1+x_5^0, 1-x_5^0+y_6^0 <= 0, cost: 2 New rule: l0 -> [6] : (-1+x_5^0-y_6^0 >= 0 /\ n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_NNiGfE.txt Applied acceleration Original rule: l0 -> l0 : x_5^0'=1+x_5^0, 1+x_5^0-y_6^0 <= 0, cost: 2 New rule: l0 -> l0 : x_5^0'=x_5^0+n0, (n0 >= 0 /\ -x_5^0-n0+y_6^0 >= 0), cost: 2*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_oPLeOF.txt Applied instantiation Original rule: l0 -> l0 : x_5^0'=x_5^0+n0, (n0 >= 0 /\ -x_5^0-n0+y_6^0 >= 0), cost: 2*n0 New rule: l0 -> l0 : x_5^0'=y_6^0, (0 >= 0 /\ -x_5^0+y_6^0 >= 0), cost: -2*x_5^0+2*y_6^0 Applied simplification Original rule: l0 -> l0 : x_5^0'=y_6^0, (0 >= 0 /\ -x_5^0+y_6^0 >= 0), cost: -2*x_5^0+2*y_6^0 New rule: l0 -> l0 : x_5^0'=y_6^0, -x_5^0+y_6^0 >= 0, cost: -2*x_5^0+2*y_6^0 Applied deletion Removed the following rules: 14 15 Accelerated simple loops Start location: l5 16: l0 -> [6] : (-1+x_5^0-y_6^0 >= 0 /\ n >= 0), cost: NONTERM 18: l0 -> l0 : x_5^0'=y_6^0, -x_5^0+y_6^0 >= 0, cost: -2*x_5^0+2*y_6^0 13: l5 -> l0 : TRUE, cost: 2 Applied chaining First rule: l5 -> l0 : TRUE, cost: 2 Second rule: l0 -> [6] : (-1+x_5^0-y_6^0 >= 0 /\ n >= 0), cost: NONTERM New rule: l5 -> [6] : -1+x_5^0-y_6^0 >= 0, cost: NONTERM Applied chaining First rule: l5 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : x_5^0'=y_6^0, -x_5^0+y_6^0 >= 0, cost: -2*x_5^0+2*y_6^0 New rule: l5 -> l0 : x_5^0'=y_6^0, -x_5^0+y_6^0 >= 0, cost: 2-2*x_5^0+2*y_6^0 Applied deletion Removed the following rules: 16 18 Chained accelerated rules with incoming rules Start location: l5 13: l5 -> l0 : TRUE, cost: 2 19: l5 -> [6] : -1+x_5^0-y_6^0 >= 0, cost: NONTERM 20: l5 -> l0 : x_5^0'=y_6^0, -x_5^0+y_6^0 >= 0, cost: 2-2*x_5^0+2*y_6^0 Removed unreachable locations and irrelevant leafs Start location: l5 19: l5 -> [6] : -1+x_5^0-y_6^0 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 19 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -1+x_5^0-y_6^0 >= 0