NO Initial ITS Start location: l4 0: l0 -> l1 : lt_8^0'=lt_8^post0, cnt_15^0'=cnt_15^post0, x_5^0'=x_5^post0, lt_7^0'=lt_7^post0, Result_4^0'=Result_4^post0, lt_9^0'=lt_9^post0, cnt_20^0'=cnt_20^post0, y_6^0'=y_6^post0, (0 == 0 /\ -cnt_20^post0+cnt_20^0 == 0 /\ lt_8^0-lt_8^post0 == 0 /\ -lt_7^post0+lt_7^0 == 0 /\ -cnt_15^post0+cnt_15^0 == 0 /\ lt_9^0-lt_9^post0 == 0 /\ Result_4^0-Result_4^post0 == 0), cost: 1 1: l1 -> l2 : lt_8^0'=lt_8^post1, cnt_15^0'=cnt_15^post1, x_5^0'=x_5^post1, lt_7^0'=lt_7^post1, Result_4^0'=Result_4^post1, lt_9^0'=lt_9^post1, cnt_20^0'=cnt_20^post1, y_6^0'=y_6^post1, (0 == 0 /\ x_5^0-x_5^post1 == 0 /\ lt_9^10-cnt_20^0 == 0 /\ -cnt_15^0+lt_8^10 == 0 /\ -y_6^post1+y_6^0 == 0 /\ -cnt_20^post1+cnt_20^0 == 0 /\ lt_9^10-lt_8^10 <= 0 /\ -lt_7^post1+lt_7^0 == 0 /\ cnt_15^0-cnt_15^post1 == 0), cost: 1 2: l1 -> l3 : lt_8^0'=lt_8^post2, cnt_15^0'=cnt_15^post2, x_5^0'=x_5^post2, lt_7^0'=lt_7^post2, Result_4^0'=Result_4^post2, lt_9^0'=lt_9^post2, cnt_20^0'=cnt_20^post2, y_6^0'=y_6^post2, (0 == 0 /\ lt_9^110-cnt_20^0 == 0 /\ -cnt_15^0+lt_7^10 == 0 /\ 1-lt_9^110+lt_8^110 <= 0 /\ -cnt_20^post2+cnt_20^0 == 0 /\ -cnt_15^0+lt_8^110 == 0 /\ -Result_4^post2+Result_4^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ -y_6^post2+y_6^0 == 0 /\ -cnt_15^post2+cnt_15^0 == 0), cost: 1 3: l3 -> l1 : lt_8^0'=lt_8^post3, cnt_15^0'=cnt_15^post3, x_5^0'=x_5^post3, lt_7^0'=lt_7^post3, Result_4^0'=Result_4^post3, lt_9^0'=lt_9^post3, cnt_20^0'=cnt_20^post3, y_6^0'=y_6^post3, (-lt_9^post3+lt_9^0 == 0 /\ lt_8^0-lt_8^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0 /\ lt_7^0-lt_7^post3 == 0 /\ -x_5^post3+x_5^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ -cnt_20^post3+cnt_20^0 == 0 /\ cnt_15^0-cnt_15^post3 == 0), cost: 1 4: l4 -> l0 : lt_8^0'=lt_8^post4, cnt_15^0'=cnt_15^post4, x_5^0'=x_5^post4, lt_7^0'=lt_7^post4, Result_4^0'=Result_4^post4, lt_9^0'=lt_9^post4, cnt_20^0'=cnt_20^post4, y_6^0'=y_6^post4, (lt_8^0-lt_8^post4 == 0 /\ -y_6^post4+y_6^0 == 0 /\ -lt_9^post4+lt_9^0 == 0 /\ -lt_7^post4+lt_7^0 == 0 /\ x_5^0-x_5^post4 == 0 /\ -cnt_15^post4+cnt_15^0 == 0 /\ -cnt_20^post4+cnt_20^0 == 0 /\ Result_4^0-Result_4^post4 == 0), cost: 1 Removed unreachable rules and leafs Start location: l4 0: l0 -> l1 : lt_8^0'=lt_8^post0, cnt_15^0'=cnt_15^post0, x_5^0'=x_5^post0, lt_7^0'=lt_7^post0, Result_4^0'=Result_4^post0, lt_9^0'=lt_9^post0, cnt_20^0'=cnt_20^post0, y_6^0'=y_6^post0, (0 == 0 /\ -cnt_20^post0+cnt_20^0 == 0 /\ lt_8^0-lt_8^post0 == 0 /\ -lt_7^post0+lt_7^0 == 0 /\ -cnt_15^post0+cnt_15^0 == 0 /\ lt_9^0-lt_9^post0 == 0 /\ Result_4^0-Result_4^post0 == 0), cost: 1 2: l1 -> l3 : lt_8^0'=lt_8^post2, cnt_15^0'=cnt_15^post2, x_5^0'=x_5^post2, lt_7^0'=lt_7^post2, Result_4^0'=Result_4^post2, lt_9^0'=lt_9^post2, cnt_20^0'=cnt_20^post2, y_6^0'=y_6^post2, (0 == 0 /\ lt_9^110-cnt_20^0 == 0 /\ -cnt_15^0+lt_7^10 == 0 /\ 1-lt_9^110+lt_8^110 <= 0 /\ -cnt_20^post2+cnt_20^0 == 0 /\ -cnt_15^0+lt_8^110 == 0 /\ -Result_4^post2+Result_4^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ -y_6^post2+y_6^0 == 0 /\ -cnt_15^post2+cnt_15^0 == 0), cost: 1 3: l3 -> l1 : lt_8^0'=lt_8^post3, cnt_15^0'=cnt_15^post3, x_5^0'=x_5^post3, lt_7^0'=lt_7^post3, Result_4^0'=Result_4^post3, lt_9^0'=lt_9^post3, cnt_20^0'=cnt_20^post3, y_6^0'=y_6^post3, (-lt_9^post3+lt_9^0 == 0 /\ lt_8^0-lt_8^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0 /\ lt_7^0-lt_7^post3 == 0 /\ -x_5^post3+x_5^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ -cnt_20^post3+cnt_20^0 == 0 /\ cnt_15^0-cnt_15^post3 == 0), cost: 1 4: l4 -> l0 : lt_8^0'=lt_8^post4, cnt_15^0'=cnt_15^post4, x_5^0'=x_5^post4, lt_7^0'=lt_7^post4, Result_4^0'=Result_4^post4, lt_9^0'=lt_9^post4, cnt_20^0'=cnt_20^post4, y_6^0'=y_6^post4, (lt_8^0-lt_8^post4 == 0 /\ -y_6^post4+y_6^0 == 0 /\ -lt_9^post4+lt_9^0 == 0 /\ -lt_7^post4+lt_7^0 == 0 /\ x_5^0-x_5^post4 == 0 /\ -cnt_15^post4+cnt_15^0 == 0 /\ -cnt_20^post4+cnt_20^0 == 0 /\ Result_4^0-Result_4^post4 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : lt_8^0'=lt_8^post0, cnt_15^0'=cnt_15^post0, x_5^0'=x_5^post0, lt_7^0'=lt_7^post0, Result_4^0'=Result_4^post0, lt_9^0'=lt_9^post0, cnt_20^0'=cnt_20^post0, y_6^0'=y_6^post0, (0 == 0 /\ -cnt_20^post0+cnt_20^0 == 0 /\ lt_8^0-lt_8^post0 == 0 /\ -lt_7^post0+lt_7^0 == 0 /\ -cnt_15^post0+cnt_15^0 == 0 /\ lt_9^0-lt_9^post0 == 0 /\ Result_4^0-Result_4^post0 == 0), cost: 1 New rule: l0 -> l1 : x_5^0'=x_5^post0, y_6^0'=y_6^post0, 0 == 0, cost: 1 Applied preprocessing Original rule: l1 -> l3 : lt_8^0'=lt_8^post2, cnt_15^0'=cnt_15^post2, x_5^0'=x_5^post2, lt_7^0'=lt_7^post2, Result_4^0'=Result_4^post2, lt_9^0'=lt_9^post2, cnt_20^0'=cnt_20^post2, y_6^0'=y_6^post2, (0 == 0 /\ lt_9^110-cnt_20^0 == 0 /\ -cnt_15^0+lt_7^10 == 0 /\ 1-lt_9^110+lt_8^110 <= 0 /\ -cnt_20^post2+cnt_20^0 == 0 /\ -cnt_15^0+lt_8^110 == 0 /\ -Result_4^post2+Result_4^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ -y_6^post2+y_6^0 == 0 /\ -cnt_15^post2+cnt_15^0 == 0), cost: 1 New rule: l1 -> l3 : lt_8^0'=lt_8^post2, lt_7^0'=lt_7^post2, lt_9^0'=lt_9^post2, 1+cnt_15^0-cnt_20^0 <= 0, cost: 1 Applied preprocessing Original rule: l3 -> l1 : lt_8^0'=lt_8^post3, cnt_15^0'=cnt_15^post3, x_5^0'=x_5^post3, lt_7^0'=lt_7^post3, Result_4^0'=Result_4^post3, lt_9^0'=lt_9^post3, cnt_20^0'=cnt_20^post3, y_6^0'=y_6^post3, (-lt_9^post3+lt_9^0 == 0 /\ lt_8^0-lt_8^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0 /\ lt_7^0-lt_7^post3 == 0 /\ -x_5^post3+x_5^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ -cnt_20^post3+cnt_20^0 == 0 /\ cnt_15^0-cnt_15^post3 == 0), cost: 1 New rule: l3 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l0 : lt_8^0'=lt_8^post4, cnt_15^0'=cnt_15^post4, x_5^0'=x_5^post4, lt_7^0'=lt_7^post4, Result_4^0'=Result_4^post4, lt_9^0'=lt_9^post4, cnt_20^0'=cnt_20^post4, y_6^0'=y_6^post4, (lt_8^0-lt_8^post4 == 0 /\ -y_6^post4+y_6^0 == 0 /\ -lt_9^post4+lt_9^0 == 0 /\ -lt_7^post4+lt_7^0 == 0 /\ x_5^0-x_5^post4 == 0 /\ -cnt_15^post4+cnt_15^0 == 0 /\ -cnt_20^post4+cnt_20^0 == 0 /\ Result_4^0-Result_4^post4 == 0), cost: 1 New rule: l4 -> l0 : TRUE, cost: 1 Simplified rules Start location: l4 5: l0 -> l1 : x_5^0'=x_5^post0, y_6^0'=y_6^post0, 0 == 0, cost: 1 6: l1 -> l3 : lt_8^0'=lt_8^post2, lt_7^0'=lt_7^post2, lt_9^0'=lt_9^post2, 1+cnt_15^0-cnt_20^0 <= 0, cost: 1 7: l3 -> l1 : TRUE, cost: 1 8: l4 -> l0 : TRUE, cost: 1 Eliminating location l0 by chaining: Applied chaining First rule: l4 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : x_5^0'=x_5^post0, y_6^0'=y_6^post0, 0 == 0, cost: 1 New rule: l4 -> l1 : x_5^0'=x_5^post0, y_6^0'=y_6^post0, 0 == 0, cost: 2 Applied deletion Removed the following rules: 5 8 Eliminating location l3 by chaining: Applied chaining First rule: l1 -> l3 : lt_8^0'=lt_8^post2, lt_7^0'=lt_7^post2, lt_9^0'=lt_9^post2, 1+cnt_15^0-cnt_20^0 <= 0, cost: 1 Second rule: l3 -> l1 : TRUE, cost: 1 New rule: l1 -> l1 : lt_8^0'=lt_8^post2, lt_7^0'=lt_7^post2, lt_9^0'=lt_9^post2, 1+cnt_15^0-cnt_20^0 <= 0, cost: 2 Applied deletion Removed the following rules: 6 7 Eliminated locations on linear paths Start location: l4 10: l1 -> l1 : lt_8^0'=lt_8^post2, lt_7^0'=lt_7^post2, lt_9^0'=lt_9^post2, 1+cnt_15^0-cnt_20^0 <= 0, cost: 2 9: l4 -> l1 : x_5^0'=x_5^post0, y_6^0'=y_6^post0, 0 == 0, cost: 2 Applied nonterm Original rule: l1 -> l1 : lt_8^0'=lt_8^post2, lt_7^0'=lt_7^post2, lt_9^0'=lt_9^post2, 1+cnt_15^0-cnt_20^0 <= 0, cost: 2 New rule: l1 -> [5] : (-1+n >= 0 /\ -1-cnt_15^0+cnt_20^0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_hjAOLF.txt Applied deletion Removed the following rules: 10 Accelerated simple loops Start location: l4 11: l1 -> [5] : (-1+n >= 0 /\ -1-cnt_15^0+cnt_20^0 >= 0), cost: NONTERM 9: l4 -> l1 : x_5^0'=x_5^post0, y_6^0'=y_6^post0, 0 == 0, cost: 2 Applied chaining First rule: l4 -> l1 : x_5^0'=x_5^post0, y_6^0'=y_6^post0, 0 == 0, cost: 2 Second rule: l1 -> [5] : (-1+n >= 0 /\ -1-cnt_15^0+cnt_20^0 >= 0), cost: NONTERM New rule: l4 -> [5] : -1-cnt_15^0+cnt_20^0 >= 0, cost: NONTERM Applied deletion Removed the following rules: 11 Chained accelerated rules with incoming rules Start location: l4 9: l4 -> l1 : x_5^0'=x_5^post0, y_6^0'=y_6^post0, 0 == 0, cost: 2 12: l4 -> [5] : -1-cnt_15^0+cnt_20^0 >= 0, cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l4 12: l4 -> [5] : -1-cnt_15^0+cnt_20^0 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 12 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -1-cnt_15^0+cnt_20^0 >= 0