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, z_7^0'=z_7^post0, (1+z_7^post0-z_7^0 == 0 /\ -1-y_6^0+y_6^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ -1-x_5^0+x_5^post0 == 0), cost: 1 1: l1 -> l0 : Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, x_5^0'=x_5^post1, z_7^0'=z_7^post1, (-x_5^post1+x_5^0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -y_6^post1+y_6^0 == 0 /\ -z_7^post1+z_7^0 == 0), cost: 1 2: l2 -> l3 : Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, x_5^0'=x_5^post2, z_7^0'=z_7^post2, (0 == 0 /\ 1+y_6^0-x_5^0 <= 0 /\ -x_5^post2+x_5^0 == 0 /\ y_6^0-y_6^post2 == 0 /\ -z_7^post2+z_7^0 == 0), cost: 1 3: l2 -> l3 : Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, x_5^0'=x_5^post3, z_7^0'=z_7^post3, (0 == 0 /\ -y_6^0+x_5^0 <= 0 /\ y_6^0-y_6^post3 == 0 /\ x_5^0-x_5^post3 == 0 /\ -z_7^post3+z_7^0 == 0 /\ 1-y_6^0+z_7^0 <= 0), cost: 1 4: l2 -> l3 : Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, x_5^0'=x_5^post4, z_7^0'=z_7^post4, (0 == 0 /\ 1+x_5^0-z_7^0 <= 0 /\ -y_6^0+x_5^0 <= 0 /\ -z_7^post4+z_7^0 == 0 /\ y_6^0-z_7^0 <= 0 /\ -x_5^post4+x_5^0 == 0 /\ -y_6^post4+y_6^0 == 0), cost: 1 5: l2 -> l0 : Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, x_5^0'=x_5^post5, z_7^0'=z_7^post5, (Result_4^0-Result_4^post5 == 0 /\ -y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-y_6^post5 == 0 /\ y_6^0-z_7^0 <= 0 /\ -z_7^post5+z_7^0 == 0 /\ -x_5^post5+x_5^0 == 0), cost: 1 6: l4 -> l2 : Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, x_5^0'=x_5^post6, z_7^0'=z_7^post6, (y_6^0-y_6^post6 == 0 /\ z_7^0-z_7^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -x_5^post6+x_5^0 == 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, z_7^0'=z_7^post0, (1+z_7^post0-z_7^0 == 0 /\ -1-y_6^0+y_6^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ -1-x_5^0+x_5^post0 == 0), cost: 1 1: l1 -> l0 : Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, x_5^0'=x_5^post1, z_7^0'=z_7^post1, (-x_5^post1+x_5^0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -y_6^post1+y_6^0 == 0 /\ -z_7^post1+z_7^0 == 0), cost: 1 5: l2 -> l0 : Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, x_5^0'=x_5^post5, z_7^0'=z_7^post5, (Result_4^0-Result_4^post5 == 0 /\ -y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-y_6^post5 == 0 /\ y_6^0-z_7^0 <= 0 /\ -z_7^post5+z_7^0 == 0 /\ -x_5^post5+x_5^0 == 0), cost: 1 6: l4 -> l2 : Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, x_5^0'=x_5^post6, z_7^0'=z_7^post6, (y_6^0-y_6^post6 == 0 /\ z_7^0-z_7^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -x_5^post6+x_5^0 == 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, z_7^0'=z_7^post0, (1+z_7^post0-z_7^0 == 0 /\ -1-y_6^0+y_6^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ -1-x_5^0+x_5^post0 == 0), cost: 1 New rule: l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l0 : Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, x_5^0'=x_5^post1, z_7^0'=z_7^post1, (-x_5^post1+x_5^0 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ -y_6^post1+y_6^0 == 0 /\ -z_7^post1+z_7^0 == 0), cost: 1 New rule: l1 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l2 -> l0 : Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, x_5^0'=x_5^post5, z_7^0'=z_7^post5, (Result_4^0-Result_4^post5 == 0 /\ -y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-y_6^post5 == 0 /\ y_6^0-z_7^0 <= 0 /\ -z_7^post5+z_7^0 == 0 /\ -x_5^post5+x_5^0 == 0), cost: 1 New rule: l2 -> l0 : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 1 Applied preprocessing Original rule: l4 -> l2 : Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, x_5^0'=x_5^post6, z_7^0'=z_7^post6, (y_6^0-y_6^post6 == 0 /\ z_7^0-z_7^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ -x_5^post6+x_5^0 == 0), cost: 1 New rule: l4 -> l2 : TRUE, cost: 1 Simplified rules Start location: l4 7: l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, TRUE, cost: 1 8: l1 -> l0 : TRUE, cost: 1 9: l2 -> l0 : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 1 10: l4 -> l2 : TRUE, cost: 1 Eliminating location l2 by chaining: Applied chaining First rule: l4 -> l2 : TRUE, cost: 1 Second rule: l2 -> l0 : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 1 New rule: l4 -> l0 : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 2 Applied deletion Removed the following rules: 9 10 Eliminating location l1 by chaining: Applied chaining First rule: l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, TRUE, cost: 1 Second rule: l1 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, TRUE, cost: 2 Applied deletion Removed the following rules: 7 8 Eliminated locations on linear paths Start location: l4 12: l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, TRUE, cost: 2 11: l4 -> l0 : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 2 Applied nonterm Original rule: l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, TRUE, cost: 2 New rule: l0 -> [5] : TRUE, cost: NONTERM Applied acceleration Original rule: l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, TRUE, cost: 2 New rule: l0 -> l0 : y_6^0'=n0+y_6^0, x_5^0'=n0+x_5^0, z_7^0'=-n0+z_7^0, TRUE, cost: 2*n0 Applied deletion Removed the following rules: 12 Accelerated simple loops Start location: l4 13: l0 -> [5] : TRUE, cost: NONTERM 14: l0 -> l0 : y_6^0'=n0+y_6^0, x_5^0'=n0+x_5^0, z_7^0'=-n0+z_7^0, TRUE, cost: 2*n0 11: l4 -> l0 : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 2 Applied chaining First rule: l4 -> l0 : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 2 Second rule: l0 -> [5] : TRUE, cost: NONTERM New rule: l4 -> [5] : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: NONTERM Applied chaining First rule: l4 -> l0 : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 2 Second rule: l0 -> l0 : y_6^0'=n0+y_6^0, x_5^0'=n0+x_5^0, z_7^0'=-n0+z_7^0, TRUE, cost: 2*n0 New rule: l4 -> l0 : y_6^0'=n0+y_6^0, x_5^0'=n0+x_5^0, z_7^0'=-n0+z_7^0, (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 2+2*n0 Applied deletion Removed the following rules: 13 14 Chained accelerated rules with incoming rules Start location: l4 11: l4 -> l0 : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 2 15: l4 -> [5] : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: NONTERM 16: l4 -> l0 : y_6^0'=n0+y_6^0, x_5^0'=n0+x_5^0, z_7^0'=-n0+z_7^0, (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: 2+2*n0 Removed unreachable locations and irrelevant leafs Start location: l4 15: l4 -> [5] : (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 15 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-y_6^0+x_5^0 <= 0 /\ -x_5^0+z_7^0 <= 0 /\ y_6^0-z_7^0 <= 0)