NO Initial ITS Start location: l7 0: l0 -> l1 : Result_4^0'=Result_4^post0, x_5^0'=x_5^post0, tmp_7^0'=tmp_7^post0, y_6^0'=y_6^post0, (0 == 0 /\ -y_6^post0+y_6^0 == 0 /\ tmp_7^0-tmp_7^post0 == 0 /\ x_5^0-x_5^post0 == 0 /\ -x_5^0+y_6^0 <= 0), cost: 1 1: l0 -> l2 : Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, tmp_7^0'=tmp_7^post1, y_6^0'=y_6^post1, (0 == 0 /\ -tmp_7^post1 <= 0 /\ tmp_7^post1 <= 0 /\ Result_4^0-Result_4^post1 == 0 /\ -1+y_6^post1-y_6^0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 3: l0 -> l4 : Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, tmp_7^0'=tmp_7^post3, y_6^0'=y_6^post3, (0 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ x_5^0-x_5^post3 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -y_6^post3+y_6^0 == 0), cost: 1 2: l2 -> l0 : Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, tmp_7^0'=tmp_7^post2, y_6^0'=y_6^post2, (-tmp_7^post2+tmp_7^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ -y_6^post2+y_6^0 == 0 /\ Result_4^0-Result_4^post2 == 0), cost: 1 4: l4 -> l5 : Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, tmp_7^0'=tmp_7^post4, y_6^0'=y_6^post4, (Result_4^0-Result_4^post4 == 0 /\ -y_6^post4+y_6^0 == 0 /\ 1+tmp_7^0 <= 0 /\ -tmp_7^post4+tmp_7^0 == 0 /\ -x_5^post4+x_5^0 == 0), cost: 1 5: l4 -> l5 : Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, tmp_7^0'=tmp_7^post5, y_6^0'=y_6^post5, (Result_4^0-Result_4^post5 == 0 /\ 1-tmp_7^0 <= 0 /\ x_5^0-x_5^post5 == 0 /\ -y_6^post5+y_6^0 == 0 /\ -tmp_7^post5+tmp_7^0 == 0), cost: 1 6: l5 -> l3 : Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, tmp_7^0'=tmp_7^post6, y_6^0'=y_6^post6, (y_6^0-y_6^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -1-x_5^0+x_5^post6 == 0 /\ -tmp_7^post6+tmp_7^0 == 0), cost: 1 7: l3 -> l0 : Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, tmp_7^0'=tmp_7^post7, y_6^0'=y_6^post7, (Result_4^0-Result_4^post7 == 0 /\ tmp_7^0-tmp_7^post7 == 0 /\ x_5^0-x_5^post7 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 8: l6 -> l0 : Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, tmp_7^0'=tmp_7^post8, y_6^0'=y_6^post8, (-y_6^post8+y_6^0 == 0 /\ -tmp_7^post8+tmp_7^0 == 0 /\ Result_4^0-Result_4^post8 == 0 /\ x_5^0-x_5^post8 == 0), cost: 1 9: l7 -> l6 : Result_4^0'=Result_4^post9, x_5^0'=x_5^post9, tmp_7^0'=tmp_7^post9, y_6^0'=y_6^post9, (-x_5^post9+x_5^0 == 0 /\ Result_4^0-Result_4^post9 == 0 /\ -y_6^post9+y_6^0 == 0 /\ -tmp_7^post9+tmp_7^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l7 1: l0 -> l2 : Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, tmp_7^0'=tmp_7^post1, y_6^0'=y_6^post1, (0 == 0 /\ -tmp_7^post1 <= 0 /\ tmp_7^post1 <= 0 /\ Result_4^0-Result_4^post1 == 0 /\ -1+y_6^post1-y_6^0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 3: l0 -> l4 : Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, tmp_7^0'=tmp_7^post3, y_6^0'=y_6^post3, (0 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ x_5^0-x_5^post3 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -y_6^post3+y_6^0 == 0), cost: 1 2: l2 -> l0 : Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, tmp_7^0'=tmp_7^post2, y_6^0'=y_6^post2, (-tmp_7^post2+tmp_7^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ -y_6^post2+y_6^0 == 0 /\ Result_4^0-Result_4^post2 == 0), cost: 1 4: l4 -> l5 : Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, tmp_7^0'=tmp_7^post4, y_6^0'=y_6^post4, (Result_4^0-Result_4^post4 == 0 /\ -y_6^post4+y_6^0 == 0 /\ 1+tmp_7^0 <= 0 /\ -tmp_7^post4+tmp_7^0 == 0 /\ -x_5^post4+x_5^0 == 0), cost: 1 5: l4 -> l5 : Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, tmp_7^0'=tmp_7^post5, y_6^0'=y_6^post5, (Result_4^0-Result_4^post5 == 0 /\ 1-tmp_7^0 <= 0 /\ x_5^0-x_5^post5 == 0 /\ -y_6^post5+y_6^0 == 0 /\ -tmp_7^post5+tmp_7^0 == 0), cost: 1 6: l5 -> l3 : Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, tmp_7^0'=tmp_7^post6, y_6^0'=y_6^post6, (y_6^0-y_6^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -1-x_5^0+x_5^post6 == 0 /\ -tmp_7^post6+tmp_7^0 == 0), cost: 1 7: l3 -> l0 : Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, tmp_7^0'=tmp_7^post7, y_6^0'=y_6^post7, (Result_4^0-Result_4^post7 == 0 /\ tmp_7^0-tmp_7^post7 == 0 /\ x_5^0-x_5^post7 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 8: l6 -> l0 : Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, tmp_7^0'=tmp_7^post8, y_6^0'=y_6^post8, (-y_6^post8+y_6^0 == 0 /\ -tmp_7^post8+tmp_7^0 == 0 /\ Result_4^0-Result_4^post8 == 0 /\ x_5^0-x_5^post8 == 0), cost: 1 9: l7 -> l6 : Result_4^0'=Result_4^post9, x_5^0'=x_5^post9, tmp_7^0'=tmp_7^post9, y_6^0'=y_6^post9, (-x_5^post9+x_5^0 == 0 /\ Result_4^0-Result_4^post9 == 0 /\ -y_6^post9+y_6^0 == 0 /\ -tmp_7^post9+tmp_7^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, tmp_7^0'=tmp_7^post1, y_6^0'=y_6^post1, (0 == 0 /\ -tmp_7^post1 <= 0 /\ tmp_7^post1 <= 0 /\ Result_4^0-Result_4^post1 == 0 /\ -1+y_6^post1-y_6^0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 New rule: l0 -> l2 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l0 : Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, tmp_7^0'=tmp_7^post2, y_6^0'=y_6^post2, (-tmp_7^post2+tmp_7^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ -y_6^post2+y_6^0 == 0 /\ Result_4^0-Result_4^post2 == 0), cost: 1 New rule: l2 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l0 -> l4 : Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, tmp_7^0'=tmp_7^post3, y_6^0'=y_6^post3, (0 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ x_5^0-x_5^post3 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ -y_6^post3+y_6^0 == 0), cost: 1 New rule: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1+x_5^0-y_6^0 <= 0, cost: 1 Applied preprocessing Original rule: l4 -> l5 : Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, tmp_7^0'=tmp_7^post4, y_6^0'=y_6^post4, (Result_4^0-Result_4^post4 == 0 /\ -y_6^post4+y_6^0 == 0 /\ 1+tmp_7^0 <= 0 /\ -tmp_7^post4+tmp_7^0 == 0 /\ -x_5^post4+x_5^0 == 0), cost: 1 New rule: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 Applied preprocessing Original rule: l4 -> l5 : Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, tmp_7^0'=tmp_7^post5, y_6^0'=y_6^post5, (Result_4^0-Result_4^post5 == 0 /\ 1-tmp_7^0 <= 0 /\ x_5^0-x_5^post5 == 0 /\ -y_6^post5+y_6^0 == 0 /\ -tmp_7^post5+tmp_7^0 == 0), cost: 1 New rule: l4 -> l5 : -1+tmp_7^0 >= 0, cost: 1 Applied preprocessing Original rule: l5 -> l3 : Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, tmp_7^0'=tmp_7^post6, y_6^0'=y_6^post6, (y_6^0-y_6^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -1-x_5^0+x_5^post6 == 0 /\ -tmp_7^post6+tmp_7^0 == 0), cost: 1 New rule: l5 -> l3 : x_5^0'=1+x_5^0, TRUE, cost: 1 Applied preprocessing Original rule: l3 -> l0 : Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, tmp_7^0'=tmp_7^post7, y_6^0'=y_6^post7, (Result_4^0-Result_4^post7 == 0 /\ tmp_7^0-tmp_7^post7 == 0 /\ x_5^0-x_5^post7 == 0 /\ -y_6^post7+y_6^0 == 0), cost: 1 New rule: l3 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l6 -> l0 : Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, tmp_7^0'=tmp_7^post8, y_6^0'=y_6^post8, (-y_6^post8+y_6^0 == 0 /\ -tmp_7^post8+tmp_7^0 == 0 /\ Result_4^0-Result_4^post8 == 0 /\ x_5^0-x_5^post8 == 0), cost: 1 New rule: l6 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l7 -> l6 : Result_4^0'=Result_4^post9, x_5^0'=x_5^post9, tmp_7^0'=tmp_7^post9, y_6^0'=y_6^post9, (-x_5^post9+x_5^0 == 0 /\ Result_4^0-Result_4^post9 == 0 /\ -y_6^post9+y_6^0 == 0 /\ -tmp_7^post9+tmp_7^0 == 0), cost: 1 New rule: l7 -> l6 : TRUE, cost: 1 Simplified rules Start location: l7 10: l0 -> l2 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 12: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1+x_5^0-y_6^0 <= 0, cost: 1 11: l2 -> l0 : TRUE, cost: 1 13: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 14: l4 -> l5 : -1+tmp_7^0 >= 0, cost: 1 15: l5 -> l3 : x_5^0'=1+x_5^0, TRUE, cost: 1 16: l3 -> l0 : TRUE, cost: 1 17: l6 -> l0 : TRUE, cost: 1 18: 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: 17 18 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 1 Second rule: l2 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 2 Applied deletion Removed the following rules: 10 11 Eliminating location l3 by chaining: Applied chaining First rule: l5 -> l3 : x_5^0'=1+x_5^0, TRUE, cost: 1 Second rule: l3 -> l0 : TRUE, cost: 1 New rule: l5 -> l0 : x_5^0'=1+x_5^0, TRUE, cost: 2 Applied deletion Removed the following rules: 15 16 Eliminated locations on linear paths Start location: l7 12: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1+x_5^0-y_6^0 <= 0, cost: 1 20: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 2 13: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 14: l4 -> l5 : -1+tmp_7^0 >= 0, cost: 1 21: l5 -> l0 : x_5^0'=1+x_5^0, TRUE, cost: 2 19: l7 -> l0 : TRUE, cost: 2 Applied nonterm Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 2 New rule: l0 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM Applied acceleration Original rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=1+y_6^0, 1+x_5^0-y_6^0 <= 0, cost: 2 New rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2*n0 Applied deletion Removed the following rules: 20 Accelerated simple loops Start location: l7 12: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1+x_5^0-y_6^0 <= 0, cost: 1 22: l0 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM 23: l0 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2*n0 13: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 14: l4 -> l5 : -1+tmp_7^0 >= 0, cost: 1 21: l5 -> l0 : x_5^0'=1+x_5^0, TRUE, cost: 2 19: l7 -> l0 : TRUE, cost: 2 Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM New rule: l7 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM Applied chaining First rule: l5 -> l0 : x_5^0'=1+x_5^0, TRUE, cost: 2 Second rule: l0 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM New rule: l5 -> [8] : -2-x_5^0+y_6^0 >= 0, cost: NONTERM Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2*n0 New rule: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Applied chaining First rule: l5 -> l0 : x_5^0'=1+x_5^0, TRUE, cost: 2 Second rule: l0 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2*n0 New rule: l5 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, -2-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Applied deletion Removed the following rules: 22 23 Chained accelerated rules with incoming rules Start location: l7 12: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1+x_5^0-y_6^0 <= 0, cost: 1 13: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 14: l4 -> l5 : -1+tmp_7^0 >= 0, cost: 1 21: l5 -> l0 : x_5^0'=1+x_5^0, TRUE, cost: 2 25: l5 -> [8] : -2-x_5^0+y_6^0 >= 0, cost: NONTERM 27: l5 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, -2-x_5^0+y_6^0 >= 0, cost: 2+2*n0 19: l7 -> l0 : TRUE, cost: 2 24: l7 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM 26: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Eliminating location l4 by chaining: Applied chaining First rule: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1+x_5^0-y_6^0 <= 0, cost: 1 Second rule: l4 -> l5 : 1+tmp_7^0 <= 0, cost: 1 New rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, (1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0), cost: 2 Applied chaining First rule: l0 -> l4 : tmp_7^0'=tmp_7^post3, 1+x_5^0-y_6^0 <= 0, cost: 1 Second rule: l4 -> l5 : -1+tmp_7^0 >= 0, cost: 1 New rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 2 Applied deletion Removed the following rules: 12 13 14 Eliminated locations on tree-shaped paths Start location: l7 28: l0 -> l5 : tmp_7^0'=tmp_7^post3, (1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0), cost: 2 29: l0 -> l5 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 2 21: l5 -> l0 : x_5^0'=1+x_5^0, TRUE, cost: 2 25: l5 -> [8] : -2-x_5^0+y_6^0 >= 0, cost: NONTERM 27: l5 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, -2-x_5^0+y_6^0 >= 0, cost: 2+2*n0 19: l7 -> l0 : TRUE, cost: 2 24: l7 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM 26: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Applied merging first rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, (1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0), cost: 2 second rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 2 new rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0)), cost: 2 Merged rules Start location: l7 30: l0 -> l5 : tmp_7^0'=tmp_7^post3, ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0)), cost: 2 21: l5 -> l0 : x_5^0'=1+x_5^0, TRUE, cost: 2 25: l5 -> [8] : -2-x_5^0+y_6^0 >= 0, cost: NONTERM 27: l5 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, -2-x_5^0+y_6^0 >= 0, cost: 2+2*n0 19: l7 -> l0 : TRUE, cost: 2 24: l7 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM 26: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Eliminating location l5 by chaining: Applied chaining First rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0)), cost: 2 Second rule: l5 -> l0 : x_5^0'=1+x_5^0, TRUE, cost: 2 New rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0)), cost: 4 Applied chaining First rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0)), cost: 2 Second rule: l5 -> [8] : -2-x_5^0+y_6^0 >= 0, cost: NONTERM New rule: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0))), cost: NONTERM Applied simplification Original rule: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0))), cost: NONTERM New rule: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied chaining First rule: l0 -> l5 : tmp_7^0'=tmp_7^post3, ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0)), cost: 2 Second rule: l5 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, -2-x_5^0+y_6^0 >= 0, cost: 2+2*n0 New rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, (-2-x_5^0+y_6^0 >= 0 /\ ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0))), cost: 4+2*n0 Applied simplification Original rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, (-2-x_5^0+y_6^0 >= 0 /\ ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0))), cost: 4+2*n0 New rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: 4+2*n0 Applied deletion Removed the following rules: 21 25 27 30 Eliminated locations on tree-shaped paths Start location: l7 31: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0)), cost: 4 32: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 33: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: 4+2*n0 19: l7 -> l0 : TRUE, cost: 2 24: l7 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM 26: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Applied simplification Original rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, ((1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0) \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0)), cost: 4 New rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ (1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0)), cost: 4 Applied simplification Original rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: 4+2*n0 New rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, (-2-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 4+2*n0 Simplified simple loops Start location: l7 32: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 34: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ (1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0)), cost: 4 35: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, (-2-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 4+2*n0 19: l7 -> l0 : TRUE, cost: 2 24: l7 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM 26: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Applied acceleration Original rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=tmp_7^post3, ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ (1+x_5^0-y_6^0 <= 0 /\ 1+tmp_7^post3 <= 0)), cost: 4 New rule: l0 -> l0 : x_5^0'=x_5^0+n4, tmp_7^0'=tmp_7^post3, (-1+n4 >= 0 /\ ((-x_5^0+y_6^0-n4 >= 0 /\ -1-tmp_7^post3 >= 0) \/ (-1+tmp_7^post3 >= 0 /\ -x_5^0+y_6^0-n4 >= 0))), cost: 4*n4 Applied instantiation Original rule: l0 -> l0 : x_5^0'=x_5^0+n4, tmp_7^0'=tmp_7^post3, (-1+n4 >= 0 /\ ((-x_5^0+y_6^0-n4 >= 0 /\ -1-tmp_7^post3 >= 0) \/ (-1+tmp_7^post3 >= 0 /\ -x_5^0+y_6^0-n4 >= 0))), cost: 4*n4 New rule: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (-1-x_5^0+y_6^0 >= 0 /\ ((0 >= 0 /\ -1+tmp_7^post3 >= 0) \/ (0 >= 0 /\ -1-tmp_7^post3 >= 0))), cost: -4*x_5^0+4*y_6^0 Applied acceleration Original rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, (-2-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 4+2*n0 New rule: l0 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+y_6^0, (-1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ -1-tmp_7^post3 >= 0)), cost: 2*n6*n0+4*n6 Applied recurrent set Original rule: l0 -> l0 : x_5^0'=1+x_5^0, tmp_7^0'=0, y_6^0'=n0+y_6^0, (-2-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 4+2*n0 New rule: l0 -> [9] : (-2-x_5^0+y_6^0 >= 0 /\ 1-n0 <= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied simplification Original rule: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (-1-x_5^0+y_6^0 >= 0 /\ ((0 >= 0 /\ -1+tmp_7^post3 >= 0) \/ (0 >= 0 /\ -1-tmp_7^post3 >= 0))), cost: -4*x_5^0+4*y_6^0 New rule: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (-1-x_5^0+y_6^0 >= 0 /\ ((0 >= 0 /\ 1+tmp_7^post3 <= 0) \/ -1+tmp_7^post3 >= 0)), cost: -4*x_5^0+4*y_6^0 Applied simplification Original rule: l0 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+y_6^0, (-1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ -1-tmp_7^post3 >= 0)), cost: 2*n6*n0+4*n6 New rule: l0 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+y_6^0, (-1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2*n6*n0+4*n6 Applied simplification Original rule: l0 -> [9] : (-2-x_5^0+y_6^0 >= 0 /\ 1-n0 <= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM New rule: l0 -> [9] : (-2-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied deletion Removed the following rules: 34 35 Accelerated simple loops Start location: l7 32: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 39: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (-1-x_5^0+y_6^0 >= 0 /\ ((0 >= 0 /\ 1+tmp_7^post3 <= 0) \/ -1+tmp_7^post3 >= 0)), cost: -4*x_5^0+4*y_6^0 40: l0 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+y_6^0, (-1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2*n6*n0+4*n6 41: l0 -> [9] : (-2-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 19: l7 -> l0 : TRUE, cost: 2 24: l7 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM 26: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 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-x_5^0+y_6^0 >= 0 /\ ((0 >= 0 /\ 1+tmp_7^post3 <= 0) \/ -1+tmp_7^post3 >= 0)), cost: -4*x_5^0+4*y_6^0 New rule: l7 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (-1-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+4*y_6^0 Applied chaining First rule: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Second rule: l0 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (-1-x_5^0+y_6^0 >= 0 /\ ((0 >= 0 /\ 1+tmp_7^post3 <= 0) \/ -1+tmp_7^post3 >= 0)), cost: -4*x_5^0+4*y_6^0 New rule: l7 -> l0 : x_5^0'=n0+y_6^0, tmp_7^0'=tmp_7^post3, y_6^0'=n0+y_6^0, (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+n0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+6*n0+4*y_6^0 Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+y_6^0, (-1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2*n6*n0+4*n6 New rule: l7 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+y_6^0, (-1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2+2*n6*n0+4*n6 Applied chaining First rule: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Second rule: l0 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+y_6^0, (-1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2*n6*n0+4*n6 New rule: l7 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+n0+y_6^0, (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+(-1+n6)*n0-n6+n0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2+2*n6*n0+4*n6+2*n0 Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> [9] : (-2-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM New rule: l7 -> [9] : (-2-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied chaining First rule: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Second rule: l0 -> [9] : (-2-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM New rule: l7 -> [9] : (-1-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied deletion Removed the following rules: 39 40 41 Chained accelerated rules with incoming rules Start location: l7 32: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 19: l7 -> l0 : TRUE, cost: 2 24: l7 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM 26: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 42: l7 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (-1-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+4*y_6^0 43: l7 -> l0 : x_5^0'=n0+y_6^0, tmp_7^0'=tmp_7^post3, y_6^0'=n0+y_6^0, (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+n0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+6*n0+4*y_6^0 44: l7 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+y_6^0, (-1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2+2*n6*n0+4*n6 45: l7 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+n0+y_6^0, (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+(-1+n6)*n0-n6+n0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2+2*n6*n0+4*n6+2*n0 46: l7 -> [9] : (-2-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 47: l7 -> [9] : (-1-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Eliminating location l0 by chaining: Applied chaining First rule: l7 -> l0 : TRUE, cost: 2 Second rule: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: NONTERM New rule: l7 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ (1+tmp_7^post3 <= 0 \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0))), cost: NONTERM Applied simplification Original rule: l7 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ (1+tmp_7^post3 <= 0 \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0))), cost: NONTERM New rule: l7 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied chaining First rule: l7 -> l0 : tmp_7^0'=0, y_6^0'=n0+y_6^0, -1-x_5^0+y_6^0 >= 0, cost: 2+2*n0 Second rule: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: NONTERM New rule: l7 -> [8] : (-1-x_5^0+y_6^0 >= 0 /\ -2-x_5^0+n0+y_6^0 >= 0 /\ (1+tmp_7^post3 <= 0 \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-n0-y_6^0 <= 0))), cost: NONTERM Applied simplification Original rule: l7 -> [8] : (-1-x_5^0+y_6^0 >= 0 /\ -2-x_5^0+n0+y_6^0 >= 0 /\ (1+tmp_7^post3 <= 0 \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-n0-y_6^0 <= 0))), cost: NONTERM New rule: l7 -> [8] : (-1-x_5^0+y_6^0 >= 0 /\ -2-x_5^0+n0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied chaining First rule: l7 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+y_6^0, (-1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2+2*n6*n0+4*n6 Second rule: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: NONTERM New rule: l7 -> [8] : (-2-x_5^0+n6*n0-n6+y_6^0 >= 0 /\ -1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (1+tmp_7^post3 <= 0 \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-n6*n0+n6-y_6^0 <= 0)) /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied simplification Original rule: l7 -> [8] : (-2-x_5^0+n6*n0-n6+y_6^0 >= 0 /\ -1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (1+tmp_7^post3 <= 0 \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-n6*n0+n6-y_6^0 <= 0)) /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM New rule: l7 -> [8] : (-2-x_5^0+n6*n0-n6+y_6^0 >= 0 /\ -1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-n6*n0+n6-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0) /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied chaining First rule: l7 -> l0 : x_5^0'=x_5^0+n6, tmp_7^0'=0, y_6^0'=n6*n0+n0+y_6^0, (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+(-1+n6)*n0-n6+n0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2+2*n6*n0+4*n6+2*n0 Second rule: l0 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0)), cost: NONTERM New rule: l7 -> [8] : (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+(-1+n6)*n0-n6+n0+y_6^0 >= 0 /\ -2-x_5^0+n6*n0-n6+n0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0) /\ (1+tmp_7^post3 <= 0 \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-n6*n0+n6-n0-y_6^0 <= 0))), cost: NONTERM Applied simplification Original rule: l7 -> [8] : (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+(-1+n6)*n0-n6+n0+y_6^0 >= 0 /\ -2-x_5^0+n6*n0-n6+n0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0) /\ (1+tmp_7^post3 <= 0 \/ (-1+tmp_7^post3 >= 0 /\ 1+x_5^0-n6*n0+n6-n0-y_6^0 <= 0))), cost: NONTERM New rule: l7 -> [8] : (-1-x_5^0+y_6^0 >= 0 /\ -2-x_5^0+n6*n0-n6+n0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM Applied partial deletion Original rule: l7 -> l0 : x_5^0'=y_6^0, tmp_7^0'=tmp_7^post3, (-1-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+4*y_6^0 New rule: l7 -> [10] : (-1-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+4*y_6^0 Applied partial deletion Original rule: l7 -> l0 : x_5^0'=n0+y_6^0, tmp_7^0'=tmp_7^post3, y_6^0'=n0+y_6^0, (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+n0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+6*n0+4*y_6^0 New rule: l7 -> [10] : (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+n0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+6*n0+4*y_6^0 Applied deletion Removed the following rules: 19 26 32 42 43 44 45 Eliminated locations on tree-shaped paths Start location: l7 24: l7 -> [8] : -1-x_5^0+y_6^0 >= 0, cost: NONTERM 46: l7 -> [9] : (-2-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 47: l7 -> [9] : (-1-x_5^0+y_6^0 >= 0 /\ -1+n0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 48: l7 -> [8] : (-2-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 49: l7 -> [8] : (-1-x_5^0+y_6^0 >= 0 /\ -2-x_5^0+n0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 50: l7 -> [8] : (-2-x_5^0+n6*n0-n6+y_6^0 >= 0 /\ -1-x_5^0+(-1+n6)*n0-n6+y_6^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ ((-1+tmp_7^post3 >= 0 /\ 1+x_5^0-n6*n0+n6-y_6^0 <= 0) \/ 1+tmp_7^post3 <= 0) /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 51: l7 -> [8] : (-1-x_5^0+y_6^0 >= 0 /\ -2-x_5^0+n6*n0-n6+n0+y_6^0 >= 0 /\ -1+n6 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: NONTERM 52: l7 -> [10] : (-1-x_5^0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+4*y_6^0 53: l7 -> [10] : (-1-x_5^0+y_6^0 >= 0 /\ -1-x_5^0+n0+y_6^0 >= 0 /\ (-1+tmp_7^post3 >= 0 \/ 1+tmp_7^post3 <= 0)), cost: 2-4*x_5^0+6*n0+4*y_6^0 Computing asymptotic complexity Proved nontermination of rule 24 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -1-x_5^0+y_6^0 >= 0