NO Initial ITS Start location: l4 0: l0 -> l1 : Result_4^0'=Result_4^post0, y_6^0'=y_6^post0, x_5^0'=x_5^post0, (Result_4^0-Result_4^post0 == 0 /\ y_6^0-y_6^post0 == 0 /\ -x_5^post0+x_5^0 == 0), cost: 1 1: l1 -> l2 : Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, x_5^0'=x_5^post1, (0 == 0 /\ y_6^0-y_6^post1 == 0 /\ 1+x_5^post1 <= 0 /\ -y_6^0-x_5^0+x_5^post1 == 0), cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, x_5^0'=x_5^post2, (y_6^0-y_6^post2 == 0 /\ -x_5^post2 <= 0 /\ -y_6^0-x_5^0+x_5^post2 == 0 /\ Result_4^0-Result_4^post2 == 0), cost: 1 3: l3 -> l1 : Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, x_5^0'=x_5^post3, (x_5^0-x_5^post3 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ y_6^0-y_6^post3 == 0), cost: 1 4: l4 -> l0 : Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, x_5^0'=x_5^post4, (y_6^0-y_6^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ Result_4^0-Result_4^post4 == 0), cost: 1 Removed unreachable rules and leafs Start location: l4 0: l0 -> l1 : Result_4^0'=Result_4^post0, y_6^0'=y_6^post0, x_5^0'=x_5^post0, (Result_4^0-Result_4^post0 == 0 /\ y_6^0-y_6^post0 == 0 /\ -x_5^post0+x_5^0 == 0), cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, x_5^0'=x_5^post2, (y_6^0-y_6^post2 == 0 /\ -x_5^post2 <= 0 /\ -y_6^0-x_5^0+x_5^post2 == 0 /\ Result_4^0-Result_4^post2 == 0), cost: 1 3: l3 -> l1 : Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, x_5^0'=x_5^post3, (x_5^0-x_5^post3 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ y_6^0-y_6^post3 == 0), cost: 1 4: l4 -> l0 : Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, x_5^0'=x_5^post4, (y_6^0-y_6^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ Result_4^0-Result_4^post4 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : Result_4^0'=Result_4^post0, y_6^0'=y_6^post0, x_5^0'=x_5^post0, (Result_4^0-Result_4^post0 == 0 /\ y_6^0-y_6^post0 == 0 /\ -x_5^post0+x_5^0 == 0), cost: 1 New rule: l0 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l3 : Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, x_5^0'=x_5^post2, (y_6^0-y_6^post2 == 0 /\ -x_5^post2 <= 0 /\ -y_6^0-x_5^0+x_5^post2 == 0 /\ Result_4^0-Result_4^post2 == 0), cost: 1 New rule: l1 -> l3 : x_5^0'=y_6^0+x_5^0, -y_6^0-x_5^0 <= 0, cost: 1 Applied preprocessing Original rule: l3 -> l1 : Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, x_5^0'=x_5^post3, (x_5^0-x_5^post3 == 0 /\ Result_4^0-Result_4^post3 == 0 /\ y_6^0-y_6^post3 == 0), cost: 1 New rule: l3 -> l1 : TRUE, cost: 1 Applied preprocessing Original rule: l4 -> l0 : Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, x_5^0'=x_5^post4, (y_6^0-y_6^post4 == 0 /\ x_5^0-x_5^post4 == 0 /\ Result_4^0-Result_4^post4 == 0), cost: 1 New rule: l4 -> l0 : TRUE, cost: 1 Simplified rules Start location: l4 5: l0 -> l1 : TRUE, cost: 1 6: l1 -> l3 : x_5^0'=y_6^0+x_5^0, -y_6^0-x_5^0 <= 0, cost: 1 7: l3 -> l1 : TRUE, cost: 1 8: l4 -> l0 : TRUE, cost: 1 Eliminating location l0 by chaining: Applied chaining First rule: l4 -> l0 : TRUE, cost: 1 Second rule: l0 -> l1 : TRUE, cost: 1 New rule: l4 -> l1 : TRUE, cost: 2 Applied deletion Removed the following rules: 5 8 Eliminating location l3 by chaining: Applied chaining First rule: l1 -> l3 : x_5^0'=y_6^0+x_5^0, -y_6^0-x_5^0 <= 0, cost: 1 Second rule: l3 -> l1 : TRUE, cost: 1 New rule: l1 -> l1 : x_5^0'=y_6^0+x_5^0, -y_6^0-x_5^0 <= 0, cost: 2 Applied deletion Removed the following rules: 6 7 Eliminated locations on linear paths Start location: l4 10: l1 -> l1 : x_5^0'=y_6^0+x_5^0, -y_6^0-x_5^0 <= 0, cost: 2 9: l4 -> l1 : TRUE, cost: 2 Applied acceleration Original rule: l1 -> l1 : x_5^0'=y_6^0+x_5^0, -y_6^0-x_5^0 <= 0, cost: 2 New rule: l1 -> l1 : x_5^0'=n0*y_6^0+x_5^0, (n0 >= 0 /\ y_6^0*(-1+n0)+y_6^0+x_5^0 >= 0 /\ y_6^0+x_5^0 >= 0), cost: 2*n0 Applied recurrent set Original rule: l1 -> l1 : x_5^0'=y_6^0+x_5^0, -y_6^0-x_5^0 <= 0, cost: 2 New rule: l1 -> [5] : (-y_6^0 <= 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM Applied fixed-point processor Original rule: l1 -> l1 : x_5^0'=y_6^0+x_5^0, -y_6^0-x_5^0 <= 0, cost: 2 New rule: l1 -> [5] : (-y_6^0 == 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM Applied simplification Original rule: l1 -> [5] : (-y_6^0 <= 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM New rule: l1 -> [5] : (y_6^0 >= 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM Applied simplification Original rule: l1 -> [5] : (-y_6^0 == 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM New rule: l1 -> [5] : (y_6^0 == 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM Applied deletion Removed the following rules: 10 Accelerated simple loops Start location: l4 11: l1 -> l1 : x_5^0'=n0*y_6^0+x_5^0, (n0 >= 0 /\ y_6^0*(-1+n0)+y_6^0+x_5^0 >= 0 /\ y_6^0+x_5^0 >= 0), cost: 2*n0 14: l1 -> [5] : (y_6^0 >= 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM 15: l1 -> [5] : (y_6^0 == 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM 9: l4 -> l1 : TRUE, cost: 2 Applied chaining First rule: l4 -> l1 : TRUE, cost: 2 Second rule: l1 -> l1 : x_5^0'=n0*y_6^0+x_5^0, (n0 >= 0 /\ y_6^0*(-1+n0)+y_6^0+x_5^0 >= 0 /\ y_6^0+x_5^0 >= 0), cost: 2*n0 New rule: l4 -> l1 : x_5^0'=n0*y_6^0+x_5^0, (n0 >= 0 /\ y_6^0*(-1+n0)+y_6^0+x_5^0 >= 0 /\ y_6^0+x_5^0 >= 0), cost: 2+2*n0 Applied chaining First rule: l4 -> l1 : TRUE, cost: 2 Second rule: l1 -> [5] : (y_6^0 >= 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM New rule: l4 -> [5] : (y_6^0 >= 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM Applied chaining First rule: l4 -> l1 : TRUE, cost: 2 Second rule: l1 -> [5] : (y_6^0 == 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM New rule: l4 -> [5] : (y_6^0 == 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM Applied deletion Removed the following rules: 11 14 15 Chained accelerated rules with incoming rules Start location: l4 9: l4 -> l1 : TRUE, cost: 2 16: l4 -> l1 : x_5^0'=n0*y_6^0+x_5^0, (n0 >= 0 /\ y_6^0*(-1+n0)+y_6^0+x_5^0 >= 0 /\ y_6^0+x_5^0 >= 0), cost: 2+2*n0 17: l4 -> [5] : (y_6^0 >= 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM 18: l4 -> [5] : (y_6^0 == 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l4 17: l4 -> [5] : (y_6^0 >= 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM 18: l4 -> [5] : (y_6^0 == 0 /\ -y_6^0-x_5^0 <= 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 17 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (y_6^0 >= 0 /\ -y_6^0-x_5^0 <= 0)