NO Initial ITS Start location: l6 0: l0 -> l2 : Result_4^0'=Result_4^post0, x_5^0'=x_5^post0, b_7^0'=b_7^post0, y_6^0'=y_6^post0, (-y_6^post0+y_6^0 == 0 /\ b_7^0-b_7^post0 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ Result_4^0-Result_4^post0 == 0 /\ x_5^0-x_5^post0 == 0), cost: 1 4: l0 -> l4 : Result_4^0'=Result_4^post4, x_5^0'=x_5^post4, b_7^0'=b_7^post4, y_6^0'=y_6^post4, (0 == 0 /\ -y_6^post4+y_6^0 == 0 /\ -b_7^post4+b_7^0 == 0 /\ -x_5^0+y_6^0 <= 0 /\ -x_5^post4+x_5^0 == 0), cost: 1 1: l2 -> l3 : Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, b_7^0'=b_7^post1, y_6^0'=y_6^post1, (-b_7^post1+b_7^0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -x_5^post1+x_5^0 == 0 /\ 1+b_7^0 <= 0 /\ -y_6^post1+y_6^0 == 0), cost: 1 2: l2 -> l3 : Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, b_7^0'=b_7^post2, y_6^0'=y_6^post2, (-b_7^post2+b_7^0 == 0 /\ 1-b_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 3: l3 -> l1 : Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, b_7^0'=b_7^post3, y_6^0'=y_6^post3, (Result_4^0-Result_4^post3 == 0 /\ -1+y_6^post3-y_6^0 == 0 /\ x_5^0-x_5^post3 == 0 /\ b_7^post3 == 0), cost: 1 6: l1 -> l0 : Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, b_7^0'=b_7^post6, y_6^0'=y_6^post6, (y_6^0-y_6^post6 == 0 /\ -b_7^0 <= 0 /\ -1+b_7^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -1-x_5^0+x_5^post6 == 0 /\ b_7^0 <= 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 7: l1 -> l4 : Result_4^0'=Result_4^post7, x_5^0'=x_5^post7, b_7^0'=b_7^post7, y_6^0'=y_6^post7, (0 == 0 /\ b_7^0-b_7^post7 == 0 /\ x_5^0-x_5^post7 == 0 /\ -y_6^post7+y_6^0 == 0 /\ -x_5^0+y_6^0 <= 0), cost: 1 5: l5 -> l1 : Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, b_7^0'=b_7^post5, y_6^0'=y_6^post5, (Result_4^0-Result_4^post5 == 0 /\ b_7^post5 == 0 /\ x_5^0-x_5^post5 == 0 /\ -y_6^post5+y_6^0 == 0), cost: 1 8: l6 -> l5 : Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, b_7^0'=b_7^post8, y_6^0'=y_6^post8, (-y_6^post8+y_6^0 == 0 /\ -b_7^post8+b_7^0 == 0 /\ Result_4^0-Result_4^post8 == 0 /\ x_5^0-x_5^post8 == 0), cost: 1 Removed unreachable rules and leafs Start location: l6 0: l0 -> l2 : Result_4^0'=Result_4^post0, x_5^0'=x_5^post0, b_7^0'=b_7^post0, y_6^0'=y_6^post0, (-y_6^post0+y_6^0 == 0 /\ b_7^0-b_7^post0 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ Result_4^0-Result_4^post0 == 0 /\ x_5^0-x_5^post0 == 0), cost: 1 1: l2 -> l3 : Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, b_7^0'=b_7^post1, y_6^0'=y_6^post1, (-b_7^post1+b_7^0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -x_5^post1+x_5^0 == 0 /\ 1+b_7^0 <= 0 /\ -y_6^post1+y_6^0 == 0), cost: 1 2: l2 -> l3 : Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, b_7^0'=b_7^post2, y_6^0'=y_6^post2, (-b_7^post2+b_7^0 == 0 /\ 1-b_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 3: l3 -> l1 : Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, b_7^0'=b_7^post3, y_6^0'=y_6^post3, (Result_4^0-Result_4^post3 == 0 /\ -1+y_6^post3-y_6^0 == 0 /\ x_5^0-x_5^post3 == 0 /\ b_7^post3 == 0), cost: 1 6: l1 -> l0 : Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, b_7^0'=b_7^post6, y_6^0'=y_6^post6, (y_6^0-y_6^post6 == 0 /\ -b_7^0 <= 0 /\ -1+b_7^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -1-x_5^0+x_5^post6 == 0 /\ b_7^0 <= 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 5: l5 -> l1 : Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, b_7^0'=b_7^post5, y_6^0'=y_6^post5, (Result_4^0-Result_4^post5 == 0 /\ b_7^post5 == 0 /\ x_5^0-x_5^post5 == 0 /\ -y_6^post5+y_6^0 == 0), cost: 1 8: l6 -> l5 : Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, b_7^0'=b_7^post8, y_6^0'=y_6^post8, (-y_6^post8+y_6^0 == 0 /\ -b_7^post8+b_7^0 == 0 /\ Result_4^0-Result_4^post8 == 0 /\ x_5^0-x_5^post8 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : Result_4^0'=Result_4^post0, x_5^0'=x_5^post0, b_7^0'=b_7^post0, y_6^0'=y_6^post0, (-y_6^post0+y_6^0 == 0 /\ b_7^0-b_7^post0 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ Result_4^0-Result_4^post0 == 0 /\ x_5^0-x_5^post0 == 0), cost: 1 New rule: l0 -> l2 : 1+x_5^0-y_6^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l3 : Result_4^0'=Result_4^post1, x_5^0'=x_5^post1, b_7^0'=b_7^post1, y_6^0'=y_6^post1, (-b_7^post1+b_7^0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -x_5^post1+x_5^0 == 0 /\ 1+b_7^0 <= 0 /\ -y_6^post1+y_6^0 == 0), cost: 1 New rule: l2 -> l3 : 1+b_7^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l3 : Result_4^0'=Result_4^post2, x_5^0'=x_5^post2, b_7^0'=b_7^post2, y_6^0'=y_6^post2, (-b_7^post2+b_7^0 == 0 /\ 1-b_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 -> l3 : -1+b_7^0 >= 0, cost: 1 Applied preprocessing Original rule: l3 -> l1 : Result_4^0'=Result_4^post3, x_5^0'=x_5^post3, b_7^0'=b_7^post3, y_6^0'=y_6^post3, (Result_4^0-Result_4^post3 == 0 /\ -1+y_6^post3-y_6^0 == 0 /\ x_5^0-x_5^post3 == 0 /\ b_7^post3 == 0), cost: 1 New rule: l3 -> l1 : b_7^0'=0, y_6^0'=1+y_6^0, TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l1 : Result_4^0'=Result_4^post5, x_5^0'=x_5^post5, b_7^0'=b_7^post5, y_6^0'=y_6^post5, (Result_4^0-Result_4^post5 == 0 /\ b_7^post5 == 0 /\ x_5^0-x_5^post5 == 0 /\ -y_6^post5+y_6^0 == 0), cost: 1 New rule: l5 -> l1 : b_7^0'=0, TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l0 : Result_4^0'=Result_4^post6, x_5^0'=x_5^post6, b_7^0'=b_7^post6, y_6^0'=y_6^post6, (y_6^0-y_6^post6 == 0 /\ -b_7^0 <= 0 /\ -1+b_7^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -1-x_5^0+x_5^post6 == 0 /\ b_7^0 <= 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 New rule: l1 -> l0 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 Applied preprocessing Original rule: l6 -> l5 : Result_4^0'=Result_4^post8, x_5^0'=x_5^post8, b_7^0'=b_7^post8, y_6^0'=y_6^post8, (-y_6^post8+y_6^0 == 0 /\ -b_7^post8+b_7^0 == 0 /\ Result_4^0-Result_4^post8 == 0 /\ x_5^0-x_5^post8 == 0), cost: 1 New rule: l6 -> l5 : TRUE, cost: 1 Simplified rules Start location: l6 9: l0 -> l2 : 1+x_5^0-y_6^0 <= 0, cost: 1 10: l2 -> l3 : 1+b_7^0 <= 0, cost: 1 11: l2 -> l3 : -1+b_7^0 >= 0, cost: 1 12: l3 -> l1 : b_7^0'=0, y_6^0'=1+y_6^0, TRUE, cost: 1 14: l1 -> l0 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 13: l5 -> l1 : b_7^0'=0, TRUE, cost: 1 15: l6 -> l5 : TRUE, cost: 1 Eliminating location l5 by chaining: Applied chaining First rule: l6 -> l5 : TRUE, cost: 1 Second rule: l5 -> l1 : b_7^0'=0, TRUE, cost: 1 New rule: l6 -> l1 : b_7^0'=0, TRUE, cost: 2 Applied deletion Removed the following rules: 13 15 Eliminating location l0 by chaining: Applied chaining First rule: l1 -> l0 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 1+x_5^0-y_6^0 <= 0), cost: 1 Second rule: l0 -> l2 : 1+x_5^0-y_6^0 <= 0, cost: 1 New rule: l1 -> l2 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 2 Applied simplification Original rule: l1 -> l2 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 1+x_5^0-y_6^0 <= 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 2 New rule: l1 -> l2 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 2 Applied deletion Removed the following rules: 9 14 Eliminated locations on linear paths Start location: l6 10: l2 -> l3 : 1+b_7^0 <= 0, cost: 1 11: l2 -> l3 : -1+b_7^0 >= 0, cost: 1 12: l3 -> l1 : b_7^0'=0, y_6^0'=1+y_6^0, TRUE, cost: 1 17: l1 -> l2 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 2 16: l6 -> l1 : b_7^0'=0, TRUE, cost: 2 Eliminating location l2 by chaining: Applied chaining First rule: l1 -> l2 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 2 Second rule: l2 -> l3 : -1+b_7^0 >= 0, cost: 1 New rule: l1 -> l3 : x_5^0'=1+x_5^0, b_7^0'=1, (0 >= 0 /\ b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 3 Applied simplification Original rule: l1 -> l3 : x_5^0'=1+x_5^0, b_7^0'=1, (0 >= 0 /\ b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 3 New rule: l1 -> l3 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 3 Applied deletion Removed the following rules: 10 11 17 Eliminated locations on tree-shaped paths Start location: l6 12: l3 -> l1 : b_7^0'=0, y_6^0'=1+y_6^0, TRUE, cost: 1 18: l1 -> l3 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 3 16: l6 -> l1 : b_7^0'=0, TRUE, cost: 2 Eliminating location l3 by chaining: Applied chaining First rule: l1 -> l3 : x_5^0'=1+x_5^0, b_7^0'=1, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 3 Second rule: l3 -> l1 : b_7^0'=0, y_6^0'=1+y_6^0, TRUE, cost: 1 New rule: l1 -> l1 : x_5^0'=1+x_5^0, b_7^0'=0, y_6^0'=1+y_6^0, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 4 Applied deletion Removed the following rules: 12 18 Eliminated locations on linear paths Start location: l6 19: l1 -> l1 : x_5^0'=1+x_5^0, b_7^0'=0, y_6^0'=1+y_6^0, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 4 16: l6 -> l1 : b_7^0'=0, TRUE, cost: 2 Applied nonterm Original rule: l1 -> l1 : x_5^0'=1+x_5^0, b_7^0'=0, y_6^0'=1+y_6^0, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 4 New rule: l1 -> [7] : (-b_7^0 >= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: NONTERM Applied acceleration Original rule: l1 -> l1 : x_5^0'=1+x_5^0, b_7^0'=0, y_6^0'=1+y_6^0, (b_7^0 == 0 /\ 2+x_5^0-y_6^0 <= 0), cost: 4 New rule: l1 -> l1 : x_5^0'=x_5^0+n0, b_7^0'=0, y_6^0'=n0+y_6^0, (-b_7^0 >= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: 4*n0 Applied simplification Original rule: l1 -> [7] : (-b_7^0 >= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: NONTERM New rule: l1 -> [7] : (b_7^0 <= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: NONTERM Applied simplification Original rule: l1 -> l1 : x_5^0'=x_5^0+n0, b_7^0'=0, y_6^0'=n0+y_6^0, (-b_7^0 >= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: 4*n0 New rule: l1 -> l1 : x_5^0'=x_5^0+n0, b_7^0'=0, y_6^0'=n0+y_6^0, (b_7^0 <= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: 4*n0 Applied deletion Removed the following rules: 19 Accelerated simple loops Start location: l6 22: l1 -> [7] : (b_7^0 <= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: NONTERM 23: l1 -> l1 : x_5^0'=x_5^0+n0, b_7^0'=0, y_6^0'=n0+y_6^0, (b_7^0 <= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: 4*n0 16: l6 -> l1 : b_7^0'=0, TRUE, cost: 2 Applied chaining First rule: l6 -> l1 : b_7^0'=0, TRUE, cost: 2 Second rule: l1 -> [7] : (b_7^0 <= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: NONTERM New rule: l6 -> [7] : -2-x_5^0+y_6^0 >= 0, cost: NONTERM Applied chaining First rule: l6 -> l1 : b_7^0'=0, TRUE, cost: 2 Second rule: l1 -> l1 : x_5^0'=x_5^0+n0, b_7^0'=0, y_6^0'=n0+y_6^0, (b_7^0 <= 0 /\ b_7^0 >= 0 /\ -2-x_5^0+y_6^0 >= 0), cost: 4*n0 New rule: l6 -> l1 : x_5^0'=x_5^0+n0, b_7^0'=0, y_6^0'=n0+y_6^0, -2-x_5^0+y_6^0 >= 0, cost: 2+4*n0 Applied deletion Removed the following rules: 22 23 Chained accelerated rules with incoming rules Start location: l6 16: l6 -> l1 : b_7^0'=0, TRUE, cost: 2 24: l6 -> [7] : -2-x_5^0+y_6^0 >= 0, cost: NONTERM 25: l6 -> l1 : x_5^0'=x_5^0+n0, b_7^0'=0, y_6^0'=n0+y_6^0, -2-x_5^0+y_6^0 >= 0, cost: 2+4*n0 Removed unreachable locations and irrelevant leafs Start location: l6 24: l6 -> [7] : -2-x_5^0+y_6^0 >= 0, cost: NONTERM 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: -2-x_5^0+y_6^0 >= 0