NO Initial ITS Start location: l7 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 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ tmp_7^post1 <= 0 /\ -tmp_7^post1 <= 0 /\ -1-y_6^0+y_6^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 -> l5 : 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: l5 -> l3 : 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 /\ -1+x_5^post5-x_5^0 == 0 /\ y_6^0-y_6^post5 == 0 /\ -Result_4^post5+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0), cost: 1 6: l3 -> 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 -> l0 : 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 8: l7 -> l6 : y_6^0'=y_6^post8, __disjvr_0^0'=__disjvr_0^post8, x_5^0'=x_5^post8, Result_4^0'=Result_4^post8, tmp_7^0'=tmp_7^post8, (-tmp_7^post8+tmp_7^0 == 0 /\ x_5^0-x_5^post8 == 0 /\ y_6^0-y_6^post8 == 0 /\ -Result_4^post8+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post8 == 0), cost: 1 Removed unreachable rules and leafs Start location: l7 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 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ tmp_7^post1 <= 0 /\ -tmp_7^post1 <= 0 /\ -1-y_6^0+y_6^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 -> l5 : 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: l5 -> l3 : 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 /\ -1+x_5^post5-x_5^0 == 0 /\ y_6^0-y_6^post5 == 0 /\ -Result_4^post5+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0), cost: 1 6: l3 -> 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 -> l0 : 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 8: l7 -> l6 : y_6^0'=y_6^post8, __disjvr_0^0'=__disjvr_0^post8, x_5^0'=x_5^post8, Result_4^0'=Result_4^post8, tmp_7^0'=tmp_7^post8, (-tmp_7^post8+tmp_7^0 == 0 /\ x_5^0-x_5^post8 == 0 /\ y_6^0-y_6^post8 == 0 /\ -Result_4^post8+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post8 == 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 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ tmp_7^post1 <= 0 /\ -tmp_7^post1 <= 0 /\ -1-y_6^0+y_6^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 -> l5 : 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 -> l5 : 0 == 0, cost: 1 Applied preprocessing Original rule: l5 -> l3 : 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 /\ -1+x_5^post5-x_5^0 == 0 /\ y_6^0-y_6^post5 == 0 /\ -Result_4^post5+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0), cost: 1 New rule: l5 -> l3 : x_5^0'=1+x_5^0, TRUE, cost: 1 Applied preprocessing Original rule: l3 -> 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: l3 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l0 : 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 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l7 -> l6 : y_6^0'=y_6^post8, __disjvr_0^0'=__disjvr_0^post8, x_5^0'=x_5^post8, Result_4^0'=Result_4^post8, tmp_7^0'=tmp_7^post8, (-tmp_7^post8+tmp_7^0 == 0 /\ x_5^0-x_5^post8 == 0 /\ y_6^0-y_6^post8 == 0 /\ -Result_4^post8+Result_4^0 == 0 /\ __disjvr_0^0-__disjvr_0^post8 == 0), cost: 1 New rule: l7 -> l6 : TRUE, cost: 1 Simplified rules Start location: l7 9: l0 -> l2 : y_6^0'=1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 1 11: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 1 10: l2 -> l0 : TRUE, cost: 1 12: l4 -> l5 : 0 == 0, cost: 1 13: l5 -> l3 : x_5^0'=1+x_5^0, TRUE, cost: 1 14: l3 -> l0 : TRUE, cost: 1 15: l6 -> l0 : TRUE, cost: 1 16: l7 -> l6 : TRUE, cost: 1 Eliminating location l6 by chaining: Applied chaining First rule: l7 -> l6 : TRUE, cost: 1 Second rule: l6 -> l0 : TRUE, cost: 1 New rule: l7 -> l0 : TRUE, cost: 2 Applied deletion Removed the following rules: 15 16 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: 9 10 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 -> l5 : 0 == 0, cost: 1 New rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, (0 == 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 Applied simplification Original rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, (0 == 0 /\ 1-y_6^0+x_5^0 <= 0), cost: 2 New rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 2 Applied deletion Removed the following rules: 11 12 Eliminating location l5 by chaining: Applied chaining First rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 2 Second rule: l5 -> l3 : x_5^0'=1+x_5^0, TRUE, cost: 1 New rule: l0 -> l3 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 3 Applied deletion Removed the following rules: 13 19 Eliminating location l3 by chaining: Applied chaining First rule: l0 -> l3 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 3 Second rule: l3 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 4 Applied deletion Removed the following rules: 14 20 Eliminated locations on linear paths Start location: l7 18: l0 -> l0 : y_6^0'=1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 2 21: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 4 17: l7 -> l0 : TRUE, cost: 2 Applied nonterm 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 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_bHAJGb.txt Applied acceleration Original rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 4 New rule: l0 -> l0 : x_5^0'=n0+x_5^0, tmp_7^0'=tmp_7^post3, (-1+n0 >= 0 /\ y_6^0-n0-x_5^0 >= 0), cost: 4*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_fnJMfC.txt Applied instantiation Original rule: l0 -> l0 : x_5^0'=n0+x_5^0, tmp_7^0'=tmp_7^post3, (-1+n0 >= 0 /\ y_6^0-n0-x_5^0 >= 0), cost: 4*n0 New rule: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (0 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: 4*y_6^0-4*x_5^0 Applied chaining First rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 4 Second 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'=1+y_6^0, x_5^0'=1+x_5^0, tmp_7^0'=0, 2-y_6^0+x_5^0 <= 0, cost: 6 Applied nonterm Original rule: l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, tmp_7^0'=0, 2-y_6^0+x_5^0 <= 0, cost: 6 New rule: l0 -> [8] : (-2+y_6^0-x_5^0 >= 0 /\ -1+n1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_HneACH.txt Applied chaining First rule: l0 -> l0 : y_6^0'=1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 2 Second rule: l0 -> [8] : (-2+y_6^0-x_5^0 >= 0 /\ -1+n1 >= 0), cost: NONTERM New rule: l0 -> [8] : (1-y_6^0+x_5^0 <= 0 /\ -1+y_6^0-x_5^0 >= 0 /\ -1+n1 >= 0), cost: NONTERM Applied chaining First rule: l0 -> l0 : y_6^0'=1+y_6^0, tmp_7^0'=0, 1-y_6^0+x_5^0 <= 0, cost: 2 Second rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 4 New rule: l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 6 Applied nonterm Original rule: l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 6 New rule: l0 -> [8] : (-1+n2 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_fIbkhM.txt Applied chaining First rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, 1-y_6^0+x_5^0 <= 0, cost: 4 Second rule: l0 -> [8] : (-1+n2 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: NONTERM New rule: l0 -> [8] : (1-y_6^0+x_5^0 <= 0 /\ -1+n2 >= 0 /\ -2+y_6^0-x_5^0 >= 0), cost: NONTERM Applied simplification Original rule: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (0 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: 4*y_6^0-4*x_5^0 New rule: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, -1+y_6^0-x_5^0 >= 0, cost: 4*y_6^0-4*x_5^0 Applied simplification Original rule: l0 -> [8] : (1-y_6^0+x_5^0 <= 0 /\ -1+y_6^0-x_5^0 >= 0 /\ -1+n1 >= 0), cost: NONTERM New rule: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ -1+n1 >= 0), cost: NONTERM Applied simplification Original rule: l0 -> [8] : (1-y_6^0+x_5^0 <= 0 /\ -1+n2 >= 0 /\ -2+y_6^0-x_5^0 >= 0), cost: NONTERM New rule: l0 -> [8] : (-1+n2 >= 0 /\ -2+y_6^0-x_5^0 >= 0), cost: NONTERM Applied deletion Removed the following rules: 18 21 Accelerated simple loops Start location: l7 22: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM 24: l0 -> [8] : (-2+y_6^0-x_5^0 >= 0 /\ -1+n1 >= 0), cost: NONTERM 26: l0 -> [8] : (-1+n2 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: NONTERM 28: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, -1+y_6^0-x_5^0 >= 0, cost: 4*y_6^0-4*x_5^0 29: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ -1+n1 >= 0), cost: NONTERM 30: l0 -> [8] : (-1+n2 >= 0 /\ -2+y_6^0-x_5^0 >= 0), cost: NONTERM 17: l7 -> l0 : TRUE, cost: 2 Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ -1+n >= 0), cost: NONTERM New rule: l7 -> [8] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> [8] : (-2+y_6^0-x_5^0 >= 0 /\ -1+n1 >= 0), cost: NONTERM New rule: l7 -> [8] : -2+y_6^0-x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> [8] : (-1+n2 >= 0 /\ -1+y_6^0-x_5^0 >= 0), cost: NONTERM New rule: l7 -> [8] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, -1+y_6^0-x_5^0 >= 0, cost: 4*y_6^0-4*x_5^0 New rule: l7 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, -1+y_6^0-x_5^0 >= 0, cost: 2+4*y_6^0-4*x_5^0 Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> [8] : (-1+y_6^0-x_5^0 >= 0 /\ -1+n1 >= 0), cost: NONTERM New rule: l7 -> [8] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> [8] : (-1+n2 >= 0 /\ -2+y_6^0-x_5^0 >= 0), cost: NONTERM New rule: l7 -> [8] : -2+y_6^0-x_5^0 >= 0, cost: NONTERM Applied deletion Removed the following rules: 22 24 26 28 29 30 Chained accelerated rules with incoming rules Start location: l7 17: l7 -> l0 : TRUE, cost: 2 31: l7 -> [8] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM 32: l7 -> [8] : -2+y_6^0-x_5^0 >= 0, cost: NONTERM 33: l7 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, -1+y_6^0-x_5^0 >= 0, cost: 2+4*y_6^0-4*x_5^0 Removed unreachable locations and irrelevant leafs Start location: l7 31: l7 -> [8] : -1+y_6^0-x_5^0 >= 0, cost: NONTERM 32: l7 -> [8] : -2+y_6^0-x_5^0 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 31 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