NO Initial ITS Start location: l4 0: l0 -> l1 : x_5^0'=x_5^post0, z_7^0'=z_7^post0, Result_4^0'=Result_4^post0, y_6^0'=y_6^post0, (1-z_7^0+z_7^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ -1-x_5^0+x_5^post0 == 0 /\ -1-y_6^0+y_6^post0 == 0), cost: 1 1: l1 -> l0 : x_5^0'=x_5^post1, z_7^0'=z_7^post1, Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, (Result_4^0-Result_4^post1 == 0 /\ z_7^0-z_7^post1 == 0 /\ x_5^0-x_5^post1 == 0 /\ -y_6^post1+y_6^0 == 0), cost: 1 2: l2 -> l3 : x_5^0'=x_5^post2, z_7^0'=z_7^post2, Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, (0 == 0 /\ -z_7^post2+z_7^0 == 0 /\ x_5^0-x_5^post2 == 0 /\ -y_6^post2+y_6^0 == 0 /\ 1-x_5^0+y_6^0 <= 0), cost: 1 3: l2 -> l3 : x_5^0'=x_5^post3, z_7^0'=z_7^post3, Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, (0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ -z_7^post3+z_7^0 == 0 /\ x_5^0-x_5^post3 == 0 /\ 1+z_7^0-y_6^0 <= 0 /\ x_5^0-y_6^0 <= 0), cost: 1 4: l2 -> l3 : x_5^0'=x_5^post4, z_7^0'=z_7^post4, Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, (0 == 0 /\ -y_6^post4+y_6^0 == 0 /\ -z_7^post4+z_7^0 == 0 /\ x_5^0-y_6^0 <= 0 /\ -x_5^post4+x_5^0 == 0 /\ 1+x_5^0-z_7^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: 1 5: l2 -> l0 : x_5^0'=x_5^post5, z_7^0'=z_7^post5, Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, (z_7^0-z_7^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ -x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ x_5^0-x_5^post5 == 0 /\ Result_4^0-Result_4^post5 == 0 /\ -z_7^0+y_6^0 <= 0), cost: 1 6: l4 -> l2 : x_5^0'=x_5^post6, z_7^0'=z_7^post6, Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, (x_5^0-x_5^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ z_7^0-z_7^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1 Removed unreachable rules and leafs Start location: l4 0: l0 -> l1 : x_5^0'=x_5^post0, z_7^0'=z_7^post0, Result_4^0'=Result_4^post0, y_6^0'=y_6^post0, (1-z_7^0+z_7^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ -1-x_5^0+x_5^post0 == 0 /\ -1-y_6^0+y_6^post0 == 0), cost: 1 1: l1 -> l0 : x_5^0'=x_5^post1, z_7^0'=z_7^post1, Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, (Result_4^0-Result_4^post1 == 0 /\ z_7^0-z_7^post1 == 0 /\ x_5^0-x_5^post1 == 0 /\ -y_6^post1+y_6^0 == 0), cost: 1 5: l2 -> l0 : x_5^0'=x_5^post5, z_7^0'=z_7^post5, Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, (z_7^0-z_7^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ -x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ x_5^0-x_5^post5 == 0 /\ Result_4^0-Result_4^post5 == 0 /\ -z_7^0+y_6^0 <= 0), cost: 1 6: l4 -> l2 : x_5^0'=x_5^post6, z_7^0'=z_7^post6, Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, (x_5^0-x_5^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ z_7^0-z_7^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l1 : x_5^0'=x_5^post0, z_7^0'=z_7^post0, Result_4^0'=Result_4^post0, y_6^0'=y_6^post0, (1-z_7^0+z_7^post0 == 0 /\ Result_4^0-Result_4^post0 == 0 /\ -1-x_5^0+x_5^post0 == 0 /\ -1-y_6^0+y_6^post0 == 0), cost: 1 New rule: l0 -> l1 : x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, y_6^0'=1+y_6^0, TRUE, cost: 1 Applied preprocessing Original rule: l1 -> l0 : x_5^0'=x_5^post1, z_7^0'=z_7^post1, Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, (Result_4^0-Result_4^post1 == 0 /\ z_7^0-z_7^post1 == 0 /\ x_5^0-x_5^post1 == 0 /\ -y_6^post1+y_6^0 == 0), cost: 1 New rule: l1 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l2 -> l0 : x_5^0'=x_5^post5, z_7^0'=z_7^post5, Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, (z_7^0-z_7^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ -x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ x_5^0-x_5^post5 == 0 /\ Result_4^0-Result_4^post5 == 0 /\ -z_7^0+y_6^0 <= 0), cost: 1 New rule: l2 -> l0 : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: 1 Applied preprocessing Original rule: l4 -> l2 : x_5^0'=x_5^post6, z_7^0'=z_7^post6, Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, (x_5^0-x_5^post6 == 0 /\ Result_4^0-Result_4^post6 == 0 /\ z_7^0-z_7^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1 New rule: l4 -> l2 : TRUE, cost: 1 Simplified rules Start location: l4 7: l0 -> l1 : x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, y_6^0'=1+y_6^0, TRUE, cost: 1 8: l1 -> l0 : TRUE, cost: 1 9: l2 -> l0 : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 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 : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: 1 New rule: l4 -> l0 : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: 2 Applied deletion Removed the following rules: 9 10 Eliminating location l1 by chaining: Applied chaining First rule: l0 -> l1 : x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, y_6^0'=1+y_6^0, TRUE, cost: 1 Second rule: l1 -> l0 : TRUE, cost: 1 New rule: l0 -> l0 : x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, y_6^0'=1+y_6^0, TRUE, cost: 2 Applied deletion Removed the following rules: 7 8 Eliminated locations on linear paths Start location: l4 12: l0 -> l0 : x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, y_6^0'=1+y_6^0, TRUE, cost: 2 11: l4 -> l0 : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: 2 Applied nonterm Original rule: l0 -> l0 : x_5^0'=1+x_5^0, z_7^0'=-1+z_7^0, y_6^0'=1+y_6^0, TRUE, cost: 2 New rule: l0 -> [5] : n >= 0, cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_EjcOfM.txt Applied deletion Removed the following rules: 12 Accelerated simple loops Start location: l4 13: l0 -> [5] : n >= 0, cost: NONTERM 11: l4 -> l0 : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: 2 Applied chaining First rule: l4 -> l0 : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: 2 Second rule: l0 -> [5] : n >= 0, cost: NONTERM New rule: l4 -> [5] : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: NONTERM Applied deletion Removed the following rules: 13 Chained accelerated rules with incoming rules Start location: l4 11: l4 -> l0 : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: 2 14: l4 -> [5] : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: l4 14: l4 -> [5] : (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 14 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-x_5^0+z_7^0 <= 0 /\ x_5^0-y_6^0 <= 0 /\ -z_7^0+y_6^0 <= 0)