NO Initial ITS Start location: l4 0: l0 -> l1 : lt_12^0'=lt_12^post0, cnt_29^0'=cnt_29^post0, y_5^0'=y_5^post0, py_6^0'=py_6^post0, lt_11^0'=lt_11^post0, Result_4^0'=Result_4^post0, x_7^0'=x_7^post0, px_8^0'=px_8^post0, lt_10^0'=lt_10^post0, q_9^0'=q_9^post0, (0 == 0 /\ cnt_29^0-cnt_29^post0 == 0 /\ -x_7^post0+x_7^0 == 0 /\ -q_9^post0+q_9^0 == 0 /\ -y_5^post0+y_5^0 == 0 /\ py_6^0-py_6^post0 == 0 /\ lt_11^10-x_7^0 == 0 /\ 1-lt_12^10 <= 0 /\ -cnt_29^0+lt_10^10 == 0 /\ lt_12^10-cnt_29^0 == 0 /\ px_8^0-px_8^post0 == 0 /\ -Result_4^post0+Result_4^0 == 0), cost: 1 2: l0 -> l2 : lt_12^0'=lt_12^post2, cnt_29^0'=cnt_29^post2, y_5^0'=y_5^post2, py_6^0'=py_6^post2, lt_11^0'=lt_11^post2, Result_4^0'=Result_4^post2, x_7^0'=x_7^post2, px_8^0'=px_8^post2, lt_10^0'=lt_10^post2, q_9^0'=q_9^post2, (0 == 0 /\ cnt_29^0-cnt_29^post2 == 0 /\ -x_7^post2+x_7^0 == 0 /\ lt_12^110 <= 0 /\ px_8^0-px_8^post2 == 0 /\ -lt_10^post2+lt_10^0 == 0 /\ -cnt_29^0+lt_12^110 == 0 /\ -y_5^post2+y_5^0 == 0 /\ -x_7^0+lt_11^11 == 0 /\ py_6^0-py_6^post2 == 0 /\ -q_9^post2+q_9^0 == 0), cost: 1 1: l1 -> l0 : lt_12^0'=lt_12^post1, cnt_29^0'=cnt_29^post1, y_5^0'=y_5^post1, py_6^0'=py_6^post1, lt_11^0'=lt_11^post1, Result_4^0'=Result_4^post1, x_7^0'=x_7^post1, px_8^0'=px_8^post1, lt_10^0'=lt_10^post1, q_9^0'=q_9^post1, (y_5^0-y_5^post1 == 0 /\ -py_6^post1+py_6^0 == 0 /\ -lt_10^post1+lt_10^0 == 0 /\ lt_12^0-lt_12^post1 == 0 /\ -px_8^post1+px_8^0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ cnt_29^0-cnt_29^post1 == 0 /\ -q_9^post1+q_9^0 == 0 /\ x_7^0-x_7^post1 == 0 /\ lt_11^0-lt_11^post1 == 0), cost: 1 3: l3 -> l0 : lt_12^0'=lt_12^post3, cnt_29^0'=cnt_29^post3, y_5^0'=y_5^post3, py_6^0'=py_6^post3, lt_11^0'=lt_11^post3, Result_4^0'=Result_4^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, lt_10^0'=lt_10^post3, q_9^0'=q_9^post3, (0 == 0 /\ -lt_10^post3+lt_10^0 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ cnt_29^0-cnt_29^post3 == 0 /\ q_9^post3-px_8^post3 == 0 /\ -lt_11^post3+lt_11^0 == 0 /\ py_6^post3-y_5^post3 == 0 /\ lt_12^0-lt_12^post3 == 0), cost: 1 4: l4 -> l3 : lt_12^0'=lt_12^post4, cnt_29^0'=cnt_29^post4, y_5^0'=y_5^post4, py_6^0'=py_6^post4, lt_11^0'=lt_11^post4, Result_4^0'=Result_4^post4, x_7^0'=x_7^post4, px_8^0'=px_8^post4, lt_10^0'=lt_10^post4, q_9^0'=q_9^post4, (cnt_29^0-cnt_29^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ x_7^0-x_7^post4 == 0 /\ -px_8^post4+px_8^0 == 0 /\ -lt_10^post4+lt_10^0 == 0 /\ -lt_11^post4+lt_11^0 == 0 /\ lt_12^0-lt_12^post4 == 0 /\ y_5^0-y_5^post4 == 0 /\ -q_9^post4+q_9^0 == 0 /\ -py_6^post4+py_6^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l4 0: l0 -> l1 : lt_12^0'=lt_12^post0, cnt_29^0'=cnt_29^post0, y_5^0'=y_5^post0, py_6^0'=py_6^post0, lt_11^0'=lt_11^post0, Result_4^0'=Result_4^post0, x_7^0'=x_7^post0, px_8^0'=px_8^post0, lt_10^0'=lt_10^post0, q_9^0'=q_9^post0, (0 == 0 /\ cnt_29^0-cnt_29^post0 == 0 /\ -x_7^post0+x_7^0 == 0 /\ -q_9^post0+q_9^0 == 0 /\ -y_5^post0+y_5^0 == 0 /\ py_6^0-py_6^post0 == 0 /\ lt_11^10-x_7^0 == 0 /\ 1-lt_12^10 <= 0 /\ -cnt_29^0+lt_10^10 == 0 /\ lt_12^10-cnt_29^0 == 0 /\ px_8^0-px_8^post0 == 0 /\ -Result_4^post0+Result_4^0 == 0), cost: 1 1: l1 -> l0 : lt_12^0'=lt_12^post1, cnt_29^0'=cnt_29^post1, y_5^0'=y_5^post1, py_6^0'=py_6^post1, lt_11^0'=lt_11^post1, Result_4^0'=Result_4^post1, x_7^0'=x_7^post1, px_8^0'=px_8^post1, lt_10^0'=lt_10^post1, q_9^0'=q_9^post1, (y_5^0-y_5^post1 == 0 /\ -py_6^post1+py_6^0 == 0 /\ -lt_10^post1+lt_10^0 == 0 /\ lt_12^0-lt_12^post1 == 0 /\ -px_8^post1+px_8^0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ cnt_29^0-cnt_29^post1 == 0 /\ -q_9^post1+q_9^0 == 0 /\ x_7^0-x_7^post1 == 0 /\ lt_11^0-lt_11^post1 == 0), cost: 1 3: l3 -> l0 : lt_12^0'=lt_12^post3, cnt_29^0'=cnt_29^post3, y_5^0'=y_5^post3, py_6^0'=py_6^post3, lt_11^0'=lt_11^post3, Result_4^0'=Result_4^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, lt_10^0'=lt_10^post3, q_9^0'=q_9^post3, (0 == 0 /\ -lt_10^post3+lt_10^0 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ cnt_29^0-cnt_29^post3 == 0 /\ q_9^post3-px_8^post3 == 0 /\ -lt_11^post3+lt_11^0 == 0 /\ py_6^post3-y_5^post3 == 0 /\ lt_12^0-lt_12^post3 == 0), cost: 1 4: l4 -> l3 : lt_12^0'=lt_12^post4, cnt_29^0'=cnt_29^post4, y_5^0'=y_5^post4, py_6^0'=py_6^post4, lt_11^0'=lt_11^post4, Result_4^0'=Result_4^post4, x_7^0'=x_7^post4, px_8^0'=px_8^post4, lt_10^0'=lt_10^post4, q_9^0'=q_9^post4, (cnt_29^0-cnt_29^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ x_7^0-x_7^post4 == 0 /\ -px_8^post4+px_8^0 == 0 /\ -lt_10^post4+lt_10^0 == 0 /\ -lt_11^post4+lt_11^0 == 0 /\ lt_12^0-lt_12^post4 == 0 /\ y_5^0-y_5^post4 == 0 /\ -q_9^post4+q_9^0 == 0 /\ -py_6^post4+py_6^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : lt_12^0'=lt_12^post0, cnt_29^0'=cnt_29^post0, y_5^0'=y_5^post0, py_6^0'=py_6^post0, lt_11^0'=lt_11^post0, Result_4^0'=Result_4^post0, x_7^0'=x_7^post0, px_8^0'=px_8^post0, lt_10^0'=lt_10^post0, q_9^0'=q_9^post0, (0 == 0 /\ cnt_29^0-cnt_29^post0 == 0 /\ -x_7^post0+x_7^0 == 0 /\ -q_9^post0+q_9^0 == 0 /\ -y_5^post0+y_5^0 == 0 /\ py_6^0-py_6^post0 == 0 /\ lt_11^10-x_7^0 == 0 /\ 1-lt_12^10 <= 0 /\ -cnt_29^0+lt_10^10 == 0 /\ lt_12^10-cnt_29^0 == 0 /\ px_8^0-px_8^post0 == 0 /\ -Result_4^post0+Result_4^0 == 0), cost: 1 New rule: l0 -> l1 : lt_12^0'=lt_12^post0, lt_11^0'=lt_11^post0, lt_10^0'=lt_10^post0, -1+cnt_29^0 >= 0, cost: 1 Applied preprocessing Original rule: l1 -> l0 : lt_12^0'=lt_12^post1, cnt_29^0'=cnt_29^post1, y_5^0'=y_5^post1, py_6^0'=py_6^post1, lt_11^0'=lt_11^post1, Result_4^0'=Result_4^post1, x_7^0'=x_7^post1, px_8^0'=px_8^post1, lt_10^0'=lt_10^post1, q_9^0'=q_9^post1, (y_5^0-y_5^post1 == 0 /\ -py_6^post1+py_6^0 == 0 /\ -lt_10^post1+lt_10^0 == 0 /\ lt_12^0-lt_12^post1 == 0 /\ -px_8^post1+px_8^0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ cnt_29^0-cnt_29^post1 == 0 /\ -q_9^post1+q_9^0 == 0 /\ x_7^0-x_7^post1 == 0 /\ lt_11^0-lt_11^post1 == 0), cost: 1 New rule: l1 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l0 : lt_12^0'=lt_12^post3, cnt_29^0'=cnt_29^post3, y_5^0'=y_5^post3, py_6^0'=py_6^post3, lt_11^0'=lt_11^post3, Result_4^0'=Result_4^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, lt_10^0'=lt_10^post3, q_9^0'=q_9^post3, (0 == 0 /\ -lt_10^post3+lt_10^0 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ cnt_29^0-cnt_29^post3 == 0 /\ q_9^post3-px_8^post3 == 0 /\ -lt_11^post3+lt_11^0 == 0 /\ py_6^post3-y_5^post3 == 0 /\ lt_12^0-lt_12^post3 == 0), cost: 1 New rule: l3 -> l0 : y_5^0'=y_5^post3, py_6^0'=y_5^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, q_9^0'=px_8^post3, 0 == 0, cost: 1 Applied preprocessing Original rule: l4 -> l3 : lt_12^0'=lt_12^post4, cnt_29^0'=cnt_29^post4, y_5^0'=y_5^post4, py_6^0'=py_6^post4, lt_11^0'=lt_11^post4, Result_4^0'=Result_4^post4, x_7^0'=x_7^post4, px_8^0'=px_8^post4, lt_10^0'=lt_10^post4, q_9^0'=q_9^post4, (cnt_29^0-cnt_29^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ x_7^0-x_7^post4 == 0 /\ -px_8^post4+px_8^0 == 0 /\ -lt_10^post4+lt_10^0 == 0 /\ -lt_11^post4+lt_11^0 == 0 /\ lt_12^0-lt_12^post4 == 0 /\ y_5^0-y_5^post4 == 0 /\ -q_9^post4+q_9^0 == 0 /\ -py_6^post4+py_6^0 == 0), cost: 1 New rule: l4 -> l3 : TRUE, cost: 1 Simplified rules Start location: l4 5: l0 -> l1 : lt_12^0'=lt_12^post0, lt_11^0'=lt_11^post0, lt_10^0'=lt_10^post0, -1+cnt_29^0 >= 0, cost: 1 6: l1 -> l0 : TRUE, cost: 1 7: l3 -> l0 : y_5^0'=y_5^post3, py_6^0'=y_5^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, q_9^0'=px_8^post3, 0 == 0, cost: 1 8: l4 -> l3 : TRUE, cost: 1 Eliminating location l3 by chaining: Applied chaining First rule: l4 -> l3 : TRUE, cost: 1 Second rule: l3 -> l0 : y_5^0'=y_5^post3, py_6^0'=y_5^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, q_9^0'=px_8^post3, 0 == 0, cost: 1 New rule: l4 -> l0 : y_5^0'=y_5^post3, py_6^0'=y_5^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, q_9^0'=px_8^post3, 0 == 0, cost: 2 Applied deletion Removed the following rules: 7 8 Eliminating location l1 by chaining: Applied chaining First rule: l0 -> l1 : lt_12^0'=lt_12^post0, lt_11^0'=lt_11^post0, lt_10^0'=lt_10^post0, -1+cnt_29^0 >= 0, cost: 1 Second rule: l1 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : lt_12^0'=lt_12^post0, lt_11^0'=lt_11^post0, lt_10^0'=lt_10^post0, -1+cnt_29^0 >= 0, cost: 2 Applied deletion Removed the following rules: 5 6 Eliminated locations on linear paths Start location: l4 10: l0 -> l0 : lt_12^0'=lt_12^post0, lt_11^0'=lt_11^post0, lt_10^0'=lt_10^post0, -1+cnt_29^0 >= 0, cost: 2 9: l4 -> l0 : y_5^0'=y_5^post3, py_6^0'=y_5^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, q_9^0'=px_8^post3, 0 == 0, cost: 2 Applied nonterm Original rule: l0 -> l0 : lt_12^0'=lt_12^post0, lt_11^0'=lt_11^post0, lt_10^0'=lt_10^post0, -1+cnt_29^0 >= 0, cost: 2 New rule: l0 -> [5] : (-1+cnt_29^0 >= 0 /\ -1+n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_NdIaNk.txt Applied deletion Removed the following rules: 10 Accelerated simple loops Start location: l4 11: l0 -> [5] : (-1+cnt_29^0 >= 0 /\ -1+n >= 0), cost: NONTERM 9: l4 -> l0 : y_5^0'=y_5^post3, py_6^0'=y_5^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, q_9^0'=px_8^post3, 0 == 0, cost: 2 Applied chaining First rule: l4 -> l0 : y_5^0'=y_5^post3, py_6^0'=y_5^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, q_9^0'=px_8^post3, 0 == 0, cost: 2 Second rule: l0 -> [5] : (-1+cnt_29^0 >= 0 /\ -1+n >= 0), cost: NONTERM New rule: l4 -> [5] : -1+cnt_29^0 >= 0, cost: NONTERM Applied deletion Removed the following rules: 11 Chained accelerated rules with incoming rules Start location: l4 9: l4 -> l0 : y_5^0'=y_5^post3, py_6^0'=y_5^post3, x_7^0'=x_7^post3, px_8^0'=px_8^post3, q_9^0'=px_8^post3, 0 == 0, cost: 2 12: l4 -> [5] : -1+cnt_29^0 >= 0, cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l4 12: l4 -> [5] : -1+cnt_29^0 >= 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_29^0 >= 0