NO Initial ITS Start location: l7 0: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post0, x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, tmp_6^0'=tmp_6^post0, (x_5^0-x_5^post0 == 0 /\ __disjvr_0^0-__disjvr_0^post0 == 0 /\ tmp_6^0-tmp_6^post0 == 0 /\ Result_4^0-Result_4^post0 == 0), cost: 1 1: l1 -> l2 : __disjvr_0^0'=__disjvr_0^post1, x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, tmp_6^0'=tmp_6^post1, (0 == 0 /\ x_5^0-x_5^post1 == 0 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ 1+x_5^0 <= 0 /\ -tmp_6^post1+tmp_6^0 == 0), cost: 1 2: l1 -> l3 : __disjvr_0^0'=__disjvr_0^post2, x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, tmp_6^0'=tmp_6^post2, (0 == 0 /\ -x_5^0 <= 0 /\ -tmp_6^post2 <= 0 /\ -x_5^post2+x_5^0 == 0 /\ __disjvr_0^0-__disjvr_0^post2 == 0 /\ tmp_6^post2 <= 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 4: l1 -> l5 : __disjvr_0^0'=__disjvr_0^post4, x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, tmp_6^0'=tmp_6^post4, (0 == 0 /\ -x_5^0 <= 0 /\ -Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+x_5^0 == 0 /\ -__disjvr_0^post4+__disjvr_0^0 == 0), cost: 1 3: l3 -> l1 : __disjvr_0^0'=__disjvr_0^post3, x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, tmp_6^0'=tmp_6^post3, (-Result_4^post3+Result_4^0 == 0 /\ -tmp_6^post3+tmp_6^0 == 0 /\ -x_5^post3+x_5^0 == 0 /\ __disjvr_0^0-__disjvr_0^post3 == 0), cost: 1 5: l5 -> l6 : __disjvr_0^0'=__disjvr_0^post5, x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, tmp_6^0'=tmp_6^post5, (x_5^0-x_5^post5 == 0 /\ tmp_6^0-tmp_6^post5 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0 /\ Result_4^0-Result_4^post5 == 0 /\ -__disjvr_0^0+__disjvr_0^post5 == 0), cost: 1 6: l6 -> l4 : __disjvr_0^0'=__disjvr_0^post6, x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, tmp_6^0'=tmp_6^post6, (__disjvr_0^0-__disjvr_0^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -tmp_6^post6+tmp_6^0 == 0 /\ 1-x_5^0+x_5^post6 == 0), cost: 1 7: l4 -> l1 : __disjvr_0^0'=__disjvr_0^post7, x_5^0'=x_5^post7, Result_4^0'=Result_4^post7, tmp_6^0'=tmp_6^post7, (-tmp_6^post7+tmp_6^0 == 0 /\ -Result_4^post7+Result_4^0 == 0 /\ -x_5^post7+x_5^0 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0), cost: 1 8: l7 -> l0 : __disjvr_0^0'=__disjvr_0^post8, x_5^0'=x_5^post8, Result_4^0'=Result_4^post8, tmp_6^0'=tmp_6^post8, (tmp_6^0-tmp_6^post8 == 0 /\ -Result_4^post8+Result_4^0 == 0 /\ -__disjvr_0^post8+__disjvr_0^0 == 0 /\ x_5^0-x_5^post8 == 0), cost: 1 Removed unreachable rules and leafs Start location: l7 0: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post0, x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, tmp_6^0'=tmp_6^post0, (x_5^0-x_5^post0 == 0 /\ __disjvr_0^0-__disjvr_0^post0 == 0 /\ tmp_6^0-tmp_6^post0 == 0 /\ Result_4^0-Result_4^post0 == 0), cost: 1 2: l1 -> l3 : __disjvr_0^0'=__disjvr_0^post2, x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, tmp_6^0'=tmp_6^post2, (0 == 0 /\ -x_5^0 <= 0 /\ -tmp_6^post2 <= 0 /\ -x_5^post2+x_5^0 == 0 /\ __disjvr_0^0-__disjvr_0^post2 == 0 /\ tmp_6^post2 <= 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 4: l1 -> l5 : __disjvr_0^0'=__disjvr_0^post4, x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, tmp_6^0'=tmp_6^post4, (0 == 0 /\ -x_5^0 <= 0 /\ -Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+x_5^0 == 0 /\ -__disjvr_0^post4+__disjvr_0^0 == 0), cost: 1 3: l3 -> l1 : __disjvr_0^0'=__disjvr_0^post3, x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, tmp_6^0'=tmp_6^post3, (-Result_4^post3+Result_4^0 == 0 /\ -tmp_6^post3+tmp_6^0 == 0 /\ -x_5^post3+x_5^0 == 0 /\ __disjvr_0^0-__disjvr_0^post3 == 0), cost: 1 5: l5 -> l6 : __disjvr_0^0'=__disjvr_0^post5, x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, tmp_6^0'=tmp_6^post5, (x_5^0-x_5^post5 == 0 /\ tmp_6^0-tmp_6^post5 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0 /\ Result_4^0-Result_4^post5 == 0 /\ -__disjvr_0^0+__disjvr_0^post5 == 0), cost: 1 6: l6 -> l4 : __disjvr_0^0'=__disjvr_0^post6, x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, tmp_6^0'=tmp_6^post6, (__disjvr_0^0-__disjvr_0^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -tmp_6^post6+tmp_6^0 == 0 /\ 1-x_5^0+x_5^post6 == 0), cost: 1 7: l4 -> l1 : __disjvr_0^0'=__disjvr_0^post7, x_5^0'=x_5^post7, Result_4^0'=Result_4^post7, tmp_6^0'=tmp_6^post7, (-tmp_6^post7+tmp_6^0 == 0 /\ -Result_4^post7+Result_4^0 == 0 /\ -x_5^post7+x_5^0 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0), cost: 1 8: l7 -> l0 : __disjvr_0^0'=__disjvr_0^post8, x_5^0'=x_5^post8, Result_4^0'=Result_4^post8, tmp_6^0'=tmp_6^post8, (tmp_6^0-tmp_6^post8 == 0 /\ -Result_4^post8+Result_4^0 == 0 /\ -__disjvr_0^post8+__disjvr_0^0 == 0 /\ x_5^0-x_5^post8 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post0, x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, tmp_6^0'=tmp_6^post0, (x_5^0-x_5^post0 == 0 /\ __disjvr_0^0-__disjvr_0^post0 == 0 /\ tmp_6^0-tmp_6^post0 == 0 /\ Result_4^0-Result_4^post0 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l3 : __disjvr_0^0'=__disjvr_0^post2, x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, tmp_6^0'=tmp_6^post2, (0 == 0 /\ -x_5^0 <= 0 /\ -tmp_6^post2 <= 0 /\ -x_5^post2+x_5^0 == 0 /\ __disjvr_0^0-__disjvr_0^post2 == 0 /\ tmp_6^post2 <= 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1 New rule: l1 -> l3 : tmp_6^0'=0, x_5^0 >= 0, cost: 1 Applied preprocessing Original rule: l3 -> l1 : __disjvr_0^0'=__disjvr_0^post3, x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, tmp_6^0'=tmp_6^post3, (-Result_4^post3+Result_4^0 == 0 /\ -tmp_6^post3+tmp_6^0 == 0 /\ -x_5^post3+x_5^0 == 0 /\ __disjvr_0^0-__disjvr_0^post3 == 0), cost: 1 New rule: l3 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l5 : __disjvr_0^0'=__disjvr_0^post4, x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, tmp_6^0'=tmp_6^post4, (0 == 0 /\ -x_5^0 <= 0 /\ -Result_4^post4+Result_4^0 == 0 /\ -x_5^post4+x_5^0 == 0 /\ -__disjvr_0^post4+__disjvr_0^0 == 0), cost: 1 New rule: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 Applied preprocessing Original rule: l5 -> l6 : __disjvr_0^0'=__disjvr_0^post5, x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, tmp_6^0'=tmp_6^post5, (x_5^0-x_5^post5 == 0 /\ tmp_6^0-tmp_6^post5 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0 /\ Result_4^0-Result_4^post5 == 0 /\ -__disjvr_0^0+__disjvr_0^post5 == 0), cost: 1 New rule: l5 -> l6 : 0 == 0, cost: 1 Applied preprocessing Original rule: l6 -> l4 : __disjvr_0^0'=__disjvr_0^post6, x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, tmp_6^0'=tmp_6^post6, (__disjvr_0^0-__disjvr_0^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -tmp_6^post6+tmp_6^0 == 0 /\ 1-x_5^0+x_5^post6 == 0), cost: 1 New rule: l6 -> l4 : x_5^0'=-1+x_5^0, TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l1 : __disjvr_0^0'=__disjvr_0^post7, x_5^0'=x_5^post7, Result_4^0'=Result_4^post7, tmp_6^0'=tmp_6^post7, (-tmp_6^post7+tmp_6^0 == 0 /\ -Result_4^post7+Result_4^0 == 0 /\ -x_5^post7+x_5^0 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0), cost: 1 New rule: l4 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l7 -> l0 : __disjvr_0^0'=__disjvr_0^post8, x_5^0'=x_5^post8, Result_4^0'=Result_4^post8, tmp_6^0'=tmp_6^post8, (tmp_6^0-tmp_6^post8 == 0 /\ -Result_4^post8+Result_4^0 == 0 /\ -__disjvr_0^post8+__disjvr_0^0 == 0 /\ x_5^0-x_5^post8 == 0), cost: 1 New rule: l7 -> l0 : TRUE, cost: 1 Simplified rules Start location: l7 9: l0 -> l1 : TRUE, cost: 1 10: l1 -> l3 : tmp_6^0'=0, x_5^0 >= 0, cost: 1 12: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 11: l3 -> l1 : TRUE, cost: 1 13: l5 -> l6 : 0 == 0, cost: 1 14: l6 -> l4 : x_5^0'=-1+x_5^0, TRUE, cost: 1 15: l4 -> l1 : TRUE, cost: 1 16: l7 -> l0 : TRUE, cost: 1 Eliminating location l0 by chaining: Applied chaining First rule: l7 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : TRUE, cost: 1 New rule: l7 -> l1 : TRUE, cost: 2 Applied deletion Removed the following rules: 9 16 Eliminating location l3 by chaining: Applied chaining First rule: l1 -> l3 : tmp_6^0'=0, x_5^0 >= 0, cost: 1 Second rule: l3 -> l1 : TRUE, cost: 1 New rule: l1 -> l1 : tmp_6^0'=0, x_5^0 >= 0, cost: 2 Applied deletion Removed the following rules: 10 11 Eliminating location l5 by chaining: Applied chaining First rule: l1 -> l5 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 1 Second rule: l5 -> l6 : 0 == 0, cost: 1 New rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, (0 == 0 /\ x_5^0 >= 0), cost: 2 Applied simplification Original rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, (0 == 0 /\ x_5^0 >= 0), cost: 2 New rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 2 Applied deletion Removed the following rules: 12 13 Eliminating location l6 by chaining: Applied chaining First rule: l1 -> l6 : tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 2 Second rule: l6 -> l4 : x_5^0'=-1+x_5^0, TRUE, cost: 1 New rule: l1 -> l4 : x_5^0'=-1+x_5^0, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 3 Applied deletion Removed the following rules: 14 19 Eliminating location l4 by chaining: Applied chaining First rule: l1 -> l4 : x_5^0'=-1+x_5^0, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 3 Second rule: l4 -> l1 : TRUE, cost: 1 New rule: l1 -> l1 : x_5^0'=-1+x_5^0, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 4 Applied deletion Removed the following rules: 15 20 Eliminated locations on linear paths Start location: l7 18: l1 -> l1 : tmp_6^0'=0, x_5^0 >= 0, cost: 2 21: l1 -> l1 : x_5^0'=-1+x_5^0, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 4 17: l7 -> l1 : TRUE, cost: 2 Applied nonterm Original rule: l1 -> l1 : tmp_6^0'=0, x_5^0 >= 0, cost: 2 New rule: l1 -> [8] : (x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_hEdOcO.txt Applied acceleration Original rule: l1 -> l1 : x_5^0'=-1+x_5^0, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 4 New rule: l1 -> l1 : x_5^0'=x_5^0-n0, tmp_6^0'=tmp_6^post4, (1+x_5^0-n0 >= 0 /\ -1+n0 >= 0), cost: 4*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_LKaIbM.txt Applied instantiation Original rule: l1 -> l1 : x_5^0'=x_5^0-n0, tmp_6^0'=tmp_6^post4, (1+x_5^0-n0 >= 0 /\ -1+n0 >= 0), cost: 4*n0 New rule: l1 -> l1 : x_5^0'=-1, tmp_6^0'=tmp_6^post4, (0 >= 0 /\ x_5^0 >= 0), cost: 4+4*x_5^0 Applied simplification Original rule: l1 -> l1 : x_5^0'=-1, tmp_6^0'=tmp_6^post4, (0 >= 0 /\ x_5^0 >= 0), cost: 4+4*x_5^0 New rule: l1 -> l1 : x_5^0'=-1, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 4+4*x_5^0 Applied deletion Removed the following rules: 18 21 Accelerated simple loops Start location: l7 22: l1 -> [8] : (x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM 24: l1 -> l1 : x_5^0'=-1, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 4+4*x_5^0 17: l7 -> l1 : TRUE, cost: 2 Applied chaining First rule: l7 -> l1 : TRUE, cost: 2 Second rule: l1 -> [8] : (x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM New rule: l7 -> [8] : x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l7 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : x_5^0'=-1, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 4+4*x_5^0 New rule: l7 -> l1 : x_5^0'=-1, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 6+4*x_5^0 Applied deletion Removed the following rules: 22 24 Chained accelerated rules with incoming rules Start location: l7 17: l7 -> l1 : TRUE, cost: 2 25: l7 -> [8] : x_5^0 >= 0, cost: NONTERM 26: l7 -> l1 : x_5^0'=-1, tmp_6^0'=tmp_6^post4, x_5^0 >= 0, cost: 6+4*x_5^0 Removed unreachable locations and irrelevant leafs Start location: l7 25: l7 -> [8] : x_5^0 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 25 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: x_5^0 >= 0