NO Initial ITS Start location: l4 0: l0 -> l1 : lt_11^0'=lt_11^post0, cnt_19^0'=cnt_19^post0, y_6^0'=y_6^post0, p2_8^0'=p2_8^post0, lt_10^0'=lt_10^post0, Result_4^0'=Result_4^post0, x_5^0'=x_5^post0, lt_9^0'=lt_9^post0, cnt_24^0'=cnt_24^post0, p_7^0'=p_7^post0, (0 == 0 /\ p2_8^0-p2_8^post0 == 0 /\ -cnt_24^post0+cnt_24^0 == 0 /\ -p_7^post0+p_7^0 == 0 /\ -x_5^post0+x_5^0 == 0 /\ -y_6^post0+y_6^0 == 0 /\ lt_10^10-cnt_19^0 == 0 /\ cnt_19^0-cnt_19^post0 == 0 /\ lt_11^10-cnt_24^0 == 0 /\ -lt_9^post0+lt_9^0 == 0 /\ -lt_10^10+lt_11^10 <= 0), cost: 1 1: l0 -> l2 : lt_11^0'=lt_11^post1, cnt_19^0'=cnt_19^post1, y_6^0'=y_6^post1, p2_8^0'=p2_8^post1, lt_10^0'=lt_10^post1, Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, lt_9^0'=lt_9^post1, cnt_24^0'=cnt_24^post1, p_7^0'=p_7^post1, (0 == 0 /\ -Result_4^post1+Result_4^0 == 0 /\ -cnt_19^0+lt_9^10 == 0 /\ -cnt_24^post1+cnt_24^0 == 0 /\ -p2_8^post1+p2_8^0 == 0 /\ cnt_19^0-cnt_19^post1 == 0 /\ -cnt_19^0+lt_10^11 == 0 /\ -p_7^post1+p_7^0 == 0 /\ -y_6^post1+y_6^0 == 0 /\ 1-lt_11^110+lt_10^11 <= 0 /\ lt_11^110-cnt_24^0 == 0 /\ -x_5^post1+x_5^0 == 0), cost: 1 2: l2 -> l0 : lt_11^0'=lt_11^post2, cnt_19^0'=cnt_19^post2, y_6^0'=y_6^post2, p2_8^0'=p2_8^post2, lt_10^0'=lt_10^post2, Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, lt_9^0'=lt_9^post2, cnt_24^0'=cnt_24^post2, p_7^0'=p_7^post2, (-p_7^post2+p_7^0 == 0 /\ y_6^0-y_6^post2 == 0 /\ -lt_9^post2+lt_9^0 == 0 /\ -cnt_24^post2+cnt_24^0 == 0 /\ -lt_10^post2+lt_10^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ lt_11^0-lt_11^post2 == 0 /\ -p2_8^post2+p2_8^0 == 0 /\ Result_4^0-Result_4^post2 == 0 /\ cnt_19^0-cnt_19^post2 == 0), cost: 1 3: l3 -> l0 : lt_11^0'=lt_11^post3, cnt_19^0'=cnt_19^post3, y_6^0'=y_6^post3, p2_8^0'=p2_8^post3, lt_10^0'=lt_10^post3, Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, lt_9^0'=lt_9^post3, cnt_24^0'=cnt_24^post3, p_7^0'=p_7^post3, (0 == 0 /\ -cnt_24^post3+cnt_24^0 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ cnt_19^0-cnt_19^post3 == 0 /\ p_7^post3-x_5^post3 == 0 /\ -lt_9^post3+lt_9^0 == 0 /\ -lt_10^post3+lt_10^0 == 0 /\ p2_8^post3-y_6^post3 == 0 /\ lt_11^0-lt_11^post3 == 0), cost: 1 4: l4 -> l3 : lt_11^0'=lt_11^post4, cnt_19^0'=cnt_19^post4, y_6^0'=y_6^post4, p2_8^0'=p2_8^post4, lt_10^0'=lt_10^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, lt_9^0'=lt_9^post4, cnt_24^0'=cnt_24^post4, p_7^0'=p_7^post4, (cnt_19^0-cnt_19^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ -lt_9^post4+lt_9^0 == 0 /\ -cnt_24^post4+cnt_24^0 == 0 /\ -lt_10^post4+lt_10^0 == 0 /\ lt_11^0-lt_11^post4 == 0 /\ y_6^0-y_6^post4 == 0 /\ -p_7^post4+p_7^0 == 0 /\ -p2_8^post4+p2_8^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l4 1: l0 -> l2 : lt_11^0'=lt_11^post1, cnt_19^0'=cnt_19^post1, y_6^0'=y_6^post1, p2_8^0'=p2_8^post1, lt_10^0'=lt_10^post1, Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, lt_9^0'=lt_9^post1, cnt_24^0'=cnt_24^post1, p_7^0'=p_7^post1, (0 == 0 /\ -Result_4^post1+Result_4^0 == 0 /\ -cnt_19^0+lt_9^10 == 0 /\ -cnt_24^post1+cnt_24^0 == 0 /\ -p2_8^post1+p2_8^0 == 0 /\ cnt_19^0-cnt_19^post1 == 0 /\ -cnt_19^0+lt_10^11 == 0 /\ -p_7^post1+p_7^0 == 0 /\ -y_6^post1+y_6^0 == 0 /\ 1-lt_11^110+lt_10^11 <= 0 /\ lt_11^110-cnt_24^0 == 0 /\ -x_5^post1+x_5^0 == 0), cost: 1 2: l2 -> l0 : lt_11^0'=lt_11^post2, cnt_19^0'=cnt_19^post2, y_6^0'=y_6^post2, p2_8^0'=p2_8^post2, lt_10^0'=lt_10^post2, Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, lt_9^0'=lt_9^post2, cnt_24^0'=cnt_24^post2, p_7^0'=p_7^post2, (-p_7^post2+p_7^0 == 0 /\ y_6^0-y_6^post2 == 0 /\ -lt_9^post2+lt_9^0 == 0 /\ -cnt_24^post2+cnt_24^0 == 0 /\ -lt_10^post2+lt_10^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ lt_11^0-lt_11^post2 == 0 /\ -p2_8^post2+p2_8^0 == 0 /\ Result_4^0-Result_4^post2 == 0 /\ cnt_19^0-cnt_19^post2 == 0), cost: 1 3: l3 -> l0 : lt_11^0'=lt_11^post3, cnt_19^0'=cnt_19^post3, y_6^0'=y_6^post3, p2_8^0'=p2_8^post3, lt_10^0'=lt_10^post3, Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, lt_9^0'=lt_9^post3, cnt_24^0'=cnt_24^post3, p_7^0'=p_7^post3, (0 == 0 /\ -cnt_24^post3+cnt_24^0 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ cnt_19^0-cnt_19^post3 == 0 /\ p_7^post3-x_5^post3 == 0 /\ -lt_9^post3+lt_9^0 == 0 /\ -lt_10^post3+lt_10^0 == 0 /\ p2_8^post3-y_6^post3 == 0 /\ lt_11^0-lt_11^post3 == 0), cost: 1 4: l4 -> l3 : lt_11^0'=lt_11^post4, cnt_19^0'=cnt_19^post4, y_6^0'=y_6^post4, p2_8^0'=p2_8^post4, lt_10^0'=lt_10^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, lt_9^0'=lt_9^post4, cnt_24^0'=cnt_24^post4, p_7^0'=p_7^post4, (cnt_19^0-cnt_19^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ -lt_9^post4+lt_9^0 == 0 /\ -cnt_24^post4+cnt_24^0 == 0 /\ -lt_10^post4+lt_10^0 == 0 /\ lt_11^0-lt_11^post4 == 0 /\ y_6^0-y_6^post4 == 0 /\ -p_7^post4+p_7^0 == 0 /\ -p2_8^post4+p2_8^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : lt_11^0'=lt_11^post1, cnt_19^0'=cnt_19^post1, y_6^0'=y_6^post1, p2_8^0'=p2_8^post1, lt_10^0'=lt_10^post1, Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, lt_9^0'=lt_9^post1, cnt_24^0'=cnt_24^post1, p_7^0'=p_7^post1, (0 == 0 /\ -Result_4^post1+Result_4^0 == 0 /\ -cnt_19^0+lt_9^10 == 0 /\ -cnt_24^post1+cnt_24^0 == 0 /\ -p2_8^post1+p2_8^0 == 0 /\ cnt_19^0-cnt_19^post1 == 0 /\ -cnt_19^0+lt_10^11 == 0 /\ -p_7^post1+p_7^0 == 0 /\ -y_6^post1+y_6^0 == 0 /\ 1-lt_11^110+lt_10^11 <= 0 /\ lt_11^110-cnt_24^0 == 0 /\ -x_5^post1+x_5^0 == 0), cost: 1 New rule: l0 -> l2 : lt_11^0'=lt_11^post1, lt_10^0'=lt_10^post1, lt_9^0'=lt_9^post1, 1+cnt_19^0-cnt_24^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l0 : lt_11^0'=lt_11^post2, cnt_19^0'=cnt_19^post2, y_6^0'=y_6^post2, p2_8^0'=p2_8^post2, lt_10^0'=lt_10^post2, Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, lt_9^0'=lt_9^post2, cnt_24^0'=cnt_24^post2, p_7^0'=p_7^post2, (-p_7^post2+p_7^0 == 0 /\ y_6^0-y_6^post2 == 0 /\ -lt_9^post2+lt_9^0 == 0 /\ -cnt_24^post2+cnt_24^0 == 0 /\ -lt_10^post2+lt_10^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ lt_11^0-lt_11^post2 == 0 /\ -p2_8^post2+p2_8^0 == 0 /\ Result_4^0-Result_4^post2 == 0 /\ cnt_19^0-cnt_19^post2 == 0), cost: 1 New rule: l2 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l0 : lt_11^0'=lt_11^post3, cnt_19^0'=cnt_19^post3, y_6^0'=y_6^post3, p2_8^0'=p2_8^post3, lt_10^0'=lt_10^post3, Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, lt_9^0'=lt_9^post3, cnt_24^0'=cnt_24^post3, p_7^0'=p_7^post3, (0 == 0 /\ -cnt_24^post3+cnt_24^0 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ cnt_19^0-cnt_19^post3 == 0 /\ p_7^post3-x_5^post3 == 0 /\ -lt_9^post3+lt_9^0 == 0 /\ -lt_10^post3+lt_10^0 == 0 /\ p2_8^post3-y_6^post3 == 0 /\ lt_11^0-lt_11^post3 == 0), cost: 1 New rule: l3 -> l0 : y_6^0'=y_6^post3, p2_8^0'=y_6^post3, x_5^0'=x_5^post3, p_7^0'=x_5^post3, 0 == 0, cost: 1 Applied preprocessing Original rule: l4 -> l3 : lt_11^0'=lt_11^post4, cnt_19^0'=cnt_19^post4, y_6^0'=y_6^post4, p2_8^0'=p2_8^post4, lt_10^0'=lt_10^post4, Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, lt_9^0'=lt_9^post4, cnt_24^0'=cnt_24^post4, p_7^0'=p_7^post4, (cnt_19^0-cnt_19^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ -lt_9^post4+lt_9^0 == 0 /\ -cnt_24^post4+cnt_24^0 == 0 /\ -lt_10^post4+lt_10^0 == 0 /\ lt_11^0-lt_11^post4 == 0 /\ y_6^0-y_6^post4 == 0 /\ -p_7^post4+p_7^0 == 0 /\ -p2_8^post4+p2_8^0 == 0), cost: 1 New rule: l4 -> l3 : TRUE, cost: 1 Simplified rules Start location: l4 5: l0 -> l2 : lt_11^0'=lt_11^post1, lt_10^0'=lt_10^post1, lt_9^0'=lt_9^post1, 1+cnt_19^0-cnt_24^0 <= 0, cost: 1 6: l2 -> l0 : TRUE, cost: 1 7: l3 -> l0 : y_6^0'=y_6^post3, p2_8^0'=y_6^post3, x_5^0'=x_5^post3, p_7^0'=x_5^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_6^0'=y_6^post3, p2_8^0'=y_6^post3, x_5^0'=x_5^post3, p_7^0'=x_5^post3, 0 == 0, cost: 1 New rule: l4 -> l0 : y_6^0'=y_6^post3, p2_8^0'=y_6^post3, x_5^0'=x_5^post3, p_7^0'=x_5^post3, 0 == 0, cost: 2 Applied deletion Removed the following rules: 7 8 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : lt_11^0'=lt_11^post1, lt_10^0'=lt_10^post1, lt_9^0'=lt_9^post1, 1+cnt_19^0-cnt_24^0 <= 0, cost: 1 Second rule: l2 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : lt_11^0'=lt_11^post1, lt_10^0'=lt_10^post1, lt_9^0'=lt_9^post1, 1+cnt_19^0-cnt_24^0 <= 0, cost: 2 Applied deletion Removed the following rules: 5 6 Eliminated locations on linear paths Start location: l4 10: l0 -> l0 : lt_11^0'=lt_11^post1, lt_10^0'=lt_10^post1, lt_9^0'=lt_9^post1, 1+cnt_19^0-cnt_24^0 <= 0, cost: 2 9: l4 -> l0 : y_6^0'=y_6^post3, p2_8^0'=y_6^post3, x_5^0'=x_5^post3, p_7^0'=x_5^post3, 0 == 0, cost: 2 Applied nonterm Original rule: l0 -> l0 : lt_11^0'=lt_11^post1, lt_10^0'=lt_10^post1, lt_9^0'=lt_9^post1, 1+cnt_19^0-cnt_24^0 <= 0, cost: 2 New rule: l0 -> [5] : (-1-cnt_19^0+cnt_24^0 >= 0 /\ -1+n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_MgAcGl.txt Applied deletion Removed the following rules: 10 Accelerated simple loops Start location: l4 11: l0 -> [5] : (-1-cnt_19^0+cnt_24^0 >= 0 /\ -1+n >= 0), cost: NONTERM 9: l4 -> l0 : y_6^0'=y_6^post3, p2_8^0'=y_6^post3, x_5^0'=x_5^post3, p_7^0'=x_5^post3, 0 == 0, cost: 2 Applied chaining First rule: l4 -> l0 : y_6^0'=y_6^post3, p2_8^0'=y_6^post3, x_5^0'=x_5^post3, p_7^0'=x_5^post3, 0 == 0, cost: 2 Second rule: l0 -> [5] : (-1-cnt_19^0+cnt_24^0 >= 0 /\ -1+n >= 0), cost: NONTERM New rule: l4 -> [5] : -1-cnt_19^0+cnt_24^0 >= 0, cost: NONTERM Applied deletion Removed the following rules: 11 Chained accelerated rules with incoming rules Start location: l4 9: l4 -> l0 : y_6^0'=y_6^post3, p2_8^0'=y_6^post3, x_5^0'=x_5^post3, p_7^0'=x_5^post3, 0 == 0, cost: 2 12: l4 -> [5] : -1-cnt_19^0+cnt_24^0 >= 0, cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l4 12: l4 -> [5] : -1-cnt_19^0+cnt_24^0 >= 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_19^0+cnt_24^0 >= 0