NO Initial ITS Start location: l6 0: l0 -> l1 : y_6^0'=y_6^post0, __disjvr_0^0'=__disjvr_0^post0, x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, tmp_7^0'=tmp_7^post0, (0 == 0 /\ -tmp_7^post0+tmp_7^0 == 0 /\ y_6^0-y_6^post0 == 0 /\ -__disjvr_0^post0+__disjvr_0^0 == 0 /\ y_6^0-x_5^0 <= 0 /\ x_5^0-x_5^post0 == 0), cost: 1 1: l0 -> l2 : y_6^0'=y_6^post1, __disjvr_0^0'=__disjvr_0^post1, x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, tmp_7^0'=tmp_7^post1, (0 == 0 /\ -Result_4^post1+Result_4^0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ 1-y_6^0+x_5^0 <= 0 /\ 1-y_6^0+y_6^post1 == 0 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ tmp_7^post1 <= 0 /\ -tmp_7^post1 <= 0), cost: 1 3: l0 -> l4 : y_6^0'=y_6^post3, __disjvr_0^0'=__disjvr_0^post3, x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, tmp_7^0'=tmp_7^post3, (0 == 0 /\ y_6^0-y_6^post3 == 0 /\ 1-y_6^0+x_5^0 <= 0 /\ __disjvr_0^0-__disjvr_0^post3 == 0 /\ x_5^0-x_5^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0), cost: 1 2: l2 -> l0 : y_6^0'=y_6^post2, __disjvr_0^0'=__disjvr_0^post2, x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, tmp_7^0'=tmp_7^post2, (y_6^0-y_6^post2 == 0 /\ -__disjvr_0^post2+__disjvr_0^0 == 0 /\ -tmp_7^post2+tmp_7^0 == 0 /\ Result_4^0-Result_4^post2 == 0 /\ x_5^0-x_5^post2 == 0), cost: 1 4: l4 -> l3 : y_6^0'=y_6^post4, __disjvr_0^0'=__disjvr_0^post4, x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, tmp_7^0'=tmp_7^post4, (-__disjvr_0^0+__disjvr_0^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ -tmp_7^post4+tmp_7^0 == 0 /\ __disjvr_0^0-__disjvr_0^post4 == 0 /\ y_6^0-y_6^post4 == 0), cost: 1 5: l3 -> l0 : y_6^0'=y_6^post5, __disjvr_0^0'=__disjvr_0^post5, x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, tmp_7^0'=tmp_7^post5, (tmp_7^0-tmp_7^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ -x_5^post5+x_5^0 == 0 /\ -Result_4^post5+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0), cost: 1 6: l5 -> l0 : y_6^0'=y_6^post6, __disjvr_0^0'=__disjvr_0^post6, x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, tmp_7^0'=tmp_7^post6, (-tmp_7^post6+tmp_7^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ y_6^0-y_6^post6 == 0 /\ -Result_4^post6+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post6 == 0), cost: 1 7: l6 -> l5 : y_6^0'=y_6^post7, __disjvr_0^0'=__disjvr_0^post7, x_5^0'=x_5^post7, Result_4^0'=Result_4^post7, tmp_7^0'=tmp_7^post7, (-x_5^post7+x_5^0 == 0 /\ tmp_7^0-tmp_7^post7 == 0 /\ Result_4^0-Result_4^post7 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0 /\ y_6^0-y_6^post7 == 0), cost: 1 Removed unreachable rules and leafs Start location: l6 1: l0 -> l2 : y_6^0'=y_6^post1, __disjvr_0^0'=__disjvr_0^post1, x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, tmp_7^0'=tmp_7^post1, (0 == 0 /\ -Result_4^post1+Result_4^0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ 1-y_6^0+x_5^0 <= 0 /\ 1-y_6^0+y_6^post1 == 0 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ tmp_7^post1 <= 0 /\ -tmp_7^post1 <= 0), cost: 1 3: l0 -> l4 : y_6^0'=y_6^post3, __disjvr_0^0'=__disjvr_0^post3, x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, tmp_7^0'=tmp_7^post3, (0 == 0 /\ y_6^0-y_6^post3 == 0 /\ 1-y_6^0+x_5^0 <= 0 /\ __disjvr_0^0-__disjvr_0^post3 == 0 /\ x_5^0-x_5^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0), cost: 1 2: l2 -> l0 : y_6^0'=y_6^post2, __disjvr_0^0'=__disjvr_0^post2, x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, tmp_7^0'=tmp_7^post2, (y_6^0-y_6^post2 == 0 /\ -__disjvr_0^post2+__disjvr_0^0 == 0 /\ -tmp_7^post2+tmp_7^0 == 0 /\ Result_4^0-Result_4^post2 == 0 /\ x_5^0-x_5^post2 == 0), cost: 1 4: l4 -> l3 : y_6^0'=y_6^post4, __disjvr_0^0'=__disjvr_0^post4, x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, tmp_7^0'=tmp_7^post4, (-__disjvr_0^0+__disjvr_0^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ -tmp_7^post4+tmp_7^0 == 0 /\ __disjvr_0^0-__disjvr_0^post4 == 0 /\ y_6^0-y_6^post4 == 0), cost: 1 5: l3 -> l0 : y_6^0'=y_6^post5, __disjvr_0^0'=__disjvr_0^post5, x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, tmp_7^0'=tmp_7^post5, (tmp_7^0-tmp_7^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ -x_5^post5+x_5^0 == 0 /\ -Result_4^post5+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0), cost: 1 6: l5 -> l0 : y_6^0'=y_6^post6, __disjvr_0^0'=__disjvr_0^post6, x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, tmp_7^0'=tmp_7^post6, (-tmp_7^post6+tmp_7^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ y_6^0-y_6^post6 == 0 /\ -Result_4^post6+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post6 == 0), cost: 1 7: l6 -> l5 : y_6^0'=y_6^post7, __disjvr_0^0'=__disjvr_0^post7, x_5^0'=x_5^post7, Result_4^0'=Result_4^post7, tmp_7^0'=tmp_7^post7, (-x_5^post7+x_5^0 == 0 /\ tmp_7^0-tmp_7^post7 == 0 /\ Result_4^0-Result_4^post7 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0 /\ y_6^0-y_6^post7 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : y_6^0'=y_6^post1, __disjvr_0^0'=__disjvr_0^post1, x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, tmp_7^0'=tmp_7^post1, (0 == 0 /\ -Result_4^post1+Result_4^0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ 1-y_6^0+x_5^0 <= 0 /\ 1-y_6^0+y_6^post1 == 0 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ tmp_7^post1 <= 0 /\ -tmp_7^post1 <= 0), cost: 1 New rule: l0 -> l2 : y_6^0'=-1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l0 : y_6^0'=y_6^post2, __disjvr_0^0'=__disjvr_0^post2, x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, tmp_7^0'=tmp_7^post2, (y_6^0-y_6^post2 == 0 /\ -__disjvr_0^post2+__disjvr_0^0 == 0 /\ -tmp_7^post2+tmp_7^0 == 0 /\ Result_4^0-Result_4^post2 == 0 /\ x_5^0-x_5^post2 == 0), cost: 1 New rule: l2 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l0 -> l4 : y_6^0'=y_6^post3, __disjvr_0^0'=__disjvr_0^post3, x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, tmp_7^0'=tmp_7^post3, (0 == 0 /\ y_6^0-y_6^post3 == 0 /\ 1-y_6^0+x_5^0 <= 0 /\ __disjvr_0^0-__disjvr_0^post3 == 0 /\ x_5^0-x_5^post3 == 0 /\ -Result_4^post3+Result_4^0 == 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 : y_6^0'=y_6^post4, __disjvr_0^0'=__disjvr_0^post4, x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, tmp_7^0'=tmp_7^post4, (-__disjvr_0^0+__disjvr_0^post4 == 0 /\ Result_4^0-Result_4^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ -tmp_7^post4+tmp_7^0 == 0 /\ __disjvr_0^0-__disjvr_0^post4 == 0 /\ y_6^0-y_6^post4 == 0), cost: 1 New rule: l4 -> l3 : 0 == 0, cost: 1 Applied preprocessing Original rule: l3 -> l0 : y_6^0'=y_6^post5, __disjvr_0^0'=__disjvr_0^post5, x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, tmp_7^0'=tmp_7^post5, (tmp_7^0-tmp_7^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ -x_5^post5+x_5^0 == 0 /\ -Result_4^post5+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0), cost: 1 New rule: l3 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l0 : y_6^0'=y_6^post6, __disjvr_0^0'=__disjvr_0^post6, x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, tmp_7^0'=tmp_7^post6, (-tmp_7^post6+tmp_7^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ y_6^0-y_6^post6 == 0 /\ -Result_4^post6+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post6 == 0), cost: 1 New rule: l5 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l5 : y_6^0'=y_6^post7, __disjvr_0^0'=__disjvr_0^post7, x_5^0'=x_5^post7, Result_4^0'=Result_4^post7, tmp_7^0'=tmp_7^post7, (-x_5^post7+x_5^0 == 0 /\ tmp_7^0-tmp_7^post7 == 0 /\ Result_4^0-Result_4^post7 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0 /\ y_6^0-y_6^post7 == 0), cost: 1 New rule: l6 -> l5 : TRUE, cost: 1 Simplified rules Start location: l6 8: l0 -> l2 : y_6^0'=-1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 1 10: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 1 9: l2 -> l0 : TRUE, cost: 1 11: l4 -> l3 : 0 == 0, cost: 1 12: l3 -> l0 : TRUE, cost: 1 13: l5 -> l0 : TRUE, cost: 1 14: 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: 13 14 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : y_6^0'=-1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 1 Second rule: l2 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : y_6^0'=-1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 2 Applied deletion Removed the following rules: 8 9 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 : 0 == 0, cost: 1 New rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, (0 == 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 Applied simplification Original rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, (0 == 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 New rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 2 Applied deletion Removed the following rules: 10 11 Eliminating location l3 by chaining: Applied chaining First rule: l0 -> l3 : tmp_7^0'=tmp_7^post3, 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-y_6^0+x_5^0 <= 0, cost: 3 Applied deletion Removed the following rules: 12 17 Eliminated locations on linear paths Start location: l6 16: l0 -> l0 : y_6^0'=-1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 2 18: l0 -> l0 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 3 15: l6 -> l0 : TRUE, cost: 2 Applied acceleration Original rule: l0 -> l0 : y_6^0'=-1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 2 New rule: l0 -> l0 : y_6^0'=y_6^0-n, tmp_7^0'=0, (y_6^0-n-x_5^0 >= 0 /\ -1+n >= 0), cost: 2*n Sub-proof via acceration calculus written to file:///tmp/tmpnam_Hpbjdi.txt Applied instantiation Original rule: l0 -> l0 : y_6^0'=y_6^0-n, tmp_7^0'=0, (y_6^0-n-x_5^0 >= 0 /\ -1+n >= 0), cost: 2*n New rule: l0 -> l0 : y_6^0'=x_5^0, tmp_7^0'=0, (0 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: 2*y_6^0-2*x_5^0 Applied nonterm Original rule: l0 -> l0 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 3 New rule: l0 -> [7] : (-1+y_6^0-x_5^0 >= 0 /\ -1+n0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_NAImiH.txt Applied simplification Original rule: l0 -> l0 : y_6^0'=x_5^0, tmp_7^0'=0, (0 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: 2*y_6^0-2*x_5^0 New rule: l0 -> l0 : y_6^0'=x_5^0, tmp_7^0'=0, -1+y_6^0-x_5^0 >= 0, cost: 2*y_6^0-2*x_5^0 Applied deletion Removed the following rules: 16 18 Accelerated simple loops Start location: l6 20: l0 -> [7] : (-1+y_6^0-x_5^0 >= 0 /\ -1+n0 >= 0), cost: NONTERM 21: l0 -> l0 : y_6^0'=x_5^0, tmp_7^0'=0, -1+y_6^0-x_5^0 >= 0, cost: 2*y_6^0-2*x_5^0 15: l6 -> l0 : TRUE, cost: 2 Applied chaining First rule: l6 -> l0 : TRUE, cost: 2 Second rule: l0 -> [7] : (-1+y_6^0-x_5^0 >= 0 /\ -1+n0 >= 0), cost: NONTERM New rule: l6 -> [7] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l6 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : y_6^0'=x_5^0, tmp_7^0'=0, -1+y_6^0-x_5^0 >= 0, cost: 2*y_6^0-2*x_5^0 New rule: l6 -> l0 : y_6^0'=x_5^0, tmp_7^0'=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 21 Chained accelerated rules with incoming rules Start location: l6 15: l6 -> l0 : TRUE, cost: 2 22: l6 -> [7] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM 23: l6 -> l0 : y_6^0'=x_5^0, tmp_7^0'=0, -1+y_6^0-x_5^0 >= 0, cost: 2+2*y_6^0-2*x_5^0 Removed unreachable locations and irrelevant leafs Start location: l6 22: l6 -> [7] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 22 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