NO Initial ITS Start location: l5 0: l0 -> l1 : y_6^0'=y_6^post0, __const_19^0'=__const_19^post0, x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, __const_29^0'=__const_29^post0, (0 == 0 /\ -__const_29^post0+__const_29^0 == 0 /\ y_6^0-y_6^post0 == 0 /\ -__const_19^post0+__const_19^0 == 0 /\ x_5^0-x_5^post0 == 0 /\ 1+__const_19^0-x_5^0 <= 0), cost: 1 1: l0 -> l2 : y_6^0'=y_6^post1, __const_19^0'=__const_19^post1, x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, __const_29^0'=__const_29^post1, (-Result_4^post1+Result_4^0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ -__const_29^post1+__const_29^0 == 0 /\ __const_19^0-__const_19^post1 == 0 /\ y_6^0-y_6^post1 == 0 /\ -__const_19^0+x_5^0 <= 0), cost: 1 3: l2 -> l0 : y_6^0'=y_6^post3, __const_19^0'=__const_19^post3, x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, __const_29^0'=__const_29^post3, (y_6^0-y_6^post3 == 0 /\ -__const_29^post3+__const_29^0 == 0 /\ 1-y_6^0+__const_29^0 <= 0 /\ __const_19^0-__const_19^post3 == 0 /\ 1-x_5^0+x_5^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0), cost: 1 4: l2 -> l4 : y_6^0'=y_6^post4, __const_19^0'=__const_19^post4, x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, __const_29^0'=__const_29^post4, (Result_4^0-Result_4^post4 == 0 /\ y_6^0-__const_29^0 <= 0 /\ -__const_29^post4+__const_29^0 == 0 /\ __const_19^0-__const_19^post4 == 0 /\ 1-x_5^0+x_5^post4 == 0 /\ y_6^0-y_6^post4 == 0), cost: 1 2: l3 -> l0 : y_6^0'=y_6^post2, __const_19^0'=__const_19^post2, x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, __const_29^0'=__const_29^post2, (y_6^0-y_6^post2 == 0 /\ -__const_19^post2+__const_19^0 == 0 /\ -__const_29^post2+__const_29^0 == 0 /\ Result_4^0-Result_4^post2 == 0 /\ x_5^0-x_5^post2 == 0), cost: 1 5: l4 -> l2 : y_6^0'=y_6^post5, __const_19^0'=__const_19^post5, x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, __const_29^0'=__const_29^post5, (__const_29^0-__const_29^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ -x_5^post5+x_5^0 == 0 /\ -Result_4^post5+Result_4^0 == 0 /\ __const_19^0-__const_19^post5 == 0), cost: 1 6: l5 -> l3 : y_6^0'=y_6^post6, __const_19^0'=__const_19^post6, x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, __const_29^0'=__const_29^post6, (-__const_29^post6+__const_29^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ y_6^0-y_6^post6 == 0 /\ -Result_4^post6+Result_4^0 == 0 /\ __const_19^0-__const_19^post6 == 0), cost: 1 Removed unreachable rules and leafs Start location: l5 1: l0 -> l2 : y_6^0'=y_6^post1, __const_19^0'=__const_19^post1, x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, __const_29^0'=__const_29^post1, (-Result_4^post1+Result_4^0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ -__const_29^post1+__const_29^0 == 0 /\ __const_19^0-__const_19^post1 == 0 /\ y_6^0-y_6^post1 == 0 /\ -__const_19^0+x_5^0 <= 0), cost: 1 3: l2 -> l0 : y_6^0'=y_6^post3, __const_19^0'=__const_19^post3, x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, __const_29^0'=__const_29^post3, (y_6^0-y_6^post3 == 0 /\ -__const_29^post3+__const_29^0 == 0 /\ 1-y_6^0+__const_29^0 <= 0 /\ __const_19^0-__const_19^post3 == 0 /\ 1-x_5^0+x_5^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0), cost: 1 4: l2 -> l4 : y_6^0'=y_6^post4, __const_19^0'=__const_19^post4, x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, __const_29^0'=__const_29^post4, (Result_4^0-Result_4^post4 == 0 /\ y_6^0-__const_29^0 <= 0 /\ -__const_29^post4+__const_29^0 == 0 /\ __const_19^0-__const_19^post4 == 0 /\ 1-x_5^0+x_5^post4 == 0 /\ y_6^0-y_6^post4 == 0), cost: 1 2: l3 -> l0 : y_6^0'=y_6^post2, __const_19^0'=__const_19^post2, x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, __const_29^0'=__const_29^post2, (y_6^0-y_6^post2 == 0 /\ -__const_19^post2+__const_19^0 == 0 /\ -__const_29^post2+__const_29^0 == 0 /\ Result_4^0-Result_4^post2 == 0 /\ x_5^0-x_5^post2 == 0), cost: 1 5: l4 -> l2 : y_6^0'=y_6^post5, __const_19^0'=__const_19^post5, x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, __const_29^0'=__const_29^post5, (__const_29^0-__const_29^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ -x_5^post5+x_5^0 == 0 /\ -Result_4^post5+Result_4^0 == 0 /\ __const_19^0-__const_19^post5 == 0), cost: 1 6: l5 -> l3 : y_6^0'=y_6^post6, __const_19^0'=__const_19^post6, x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, __const_29^0'=__const_29^post6, (-__const_29^post6+__const_29^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ y_6^0-y_6^post6 == 0 /\ -Result_4^post6+Result_4^0 == 0 /\ __const_19^0-__const_19^post6 == 0), cost: 1 Applied preprocessing Original rule: l0 -> l2 : y_6^0'=y_6^post1, __const_19^0'=__const_19^post1, x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, __const_29^0'=__const_29^post1, (-Result_4^post1+Result_4^0 == 0 /\ -x_5^post1+x_5^0 == 0 /\ -__const_29^post1+__const_29^0 == 0 /\ __const_19^0-__const_19^post1 == 0 /\ y_6^0-y_6^post1 == 0 /\ -__const_19^0+x_5^0 <= 0), cost: 1 New rule: l0 -> l2 : -__const_19^0+x_5^0 <= 0, cost: 1 Applied preprocessing Original rule: l3 -> l0 : y_6^0'=y_6^post2, __const_19^0'=__const_19^post2, x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, __const_29^0'=__const_29^post2, (y_6^0-y_6^post2 == 0 /\ -__const_19^post2+__const_19^0 == 0 /\ -__const_29^post2+__const_29^0 == 0 /\ Result_4^0-Result_4^post2 == 0 /\ x_5^0-x_5^post2 == 0), cost: 1 New rule: l3 -> l0 : TRUE, cost: 1 Applied preprocessing Original rule: l2 -> l0 : y_6^0'=y_6^post3, __const_19^0'=__const_19^post3, x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, __const_29^0'=__const_29^post3, (y_6^0-y_6^post3 == 0 /\ -__const_29^post3+__const_29^0 == 0 /\ 1-y_6^0+__const_29^0 <= 0 /\ __const_19^0-__const_19^post3 == 0 /\ 1-x_5^0+x_5^post3 == 0 /\ -Result_4^post3+Result_4^0 == 0), cost: 1 New rule: l2 -> l0 : x_5^0'=-1+x_5^0, 1-y_6^0+__const_29^0 <= 0, cost: 1 Applied preprocessing Original rule: l2 -> l4 : y_6^0'=y_6^post4, __const_19^0'=__const_19^post4, x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, __const_29^0'=__const_29^post4, (Result_4^0-Result_4^post4 == 0 /\ y_6^0-__const_29^0 <= 0 /\ -__const_29^post4+__const_29^0 == 0 /\ __const_19^0-__const_19^post4 == 0 /\ 1-x_5^0+x_5^post4 == 0 /\ y_6^0-y_6^post4 == 0), cost: 1 New rule: l2 -> l4 : x_5^0'=-1+x_5^0, y_6^0-__const_29^0 <= 0, cost: 1 Applied preprocessing Original rule: l4 -> l2 : y_6^0'=y_6^post5, __const_19^0'=__const_19^post5, x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, __const_29^0'=__const_29^post5, (__const_29^0-__const_29^post5 == 0 /\ y_6^0-y_6^post5 == 0 /\ -x_5^post5+x_5^0 == 0 /\ -Result_4^post5+Result_4^0 == 0 /\ __const_19^0-__const_19^post5 == 0), cost: 1 New rule: l4 -> l2 : TRUE, cost: 1 Applied preprocessing Original rule: l5 -> l3 : y_6^0'=y_6^post6, __const_19^0'=__const_19^post6, x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, __const_29^0'=__const_29^post6, (-__const_29^post6+__const_29^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ y_6^0-y_6^post6 == 0 /\ -Result_4^post6+Result_4^0 == 0 /\ __const_19^0-__const_19^post6 == 0), cost: 1 New rule: l5 -> l3 : TRUE, cost: 1 Simplified rules Start location: l5 7: l0 -> l2 : -__const_19^0+x_5^0 <= 0, cost: 1 9: l2 -> l0 : x_5^0'=-1+x_5^0, 1-y_6^0+__const_29^0 <= 0, cost: 1 10: l2 -> l4 : x_5^0'=-1+x_5^0, y_6^0-__const_29^0 <= 0, cost: 1 8: l3 -> l0 : TRUE, cost: 1 11: l4 -> l2 : TRUE, cost: 1 12: l5 -> l3 : TRUE, cost: 1 Eliminating location l3 by chaining: Applied chaining First rule: l5 -> l3 : TRUE, cost: 1 Second rule: l3 -> l0 : TRUE, cost: 1 New rule: l5 -> l0 : TRUE, cost: 2 Applied deletion Removed the following rules: 8 12 Eliminating location l4 by chaining: Applied chaining First rule: l2 -> l4 : x_5^0'=-1+x_5^0, y_6^0-__const_29^0 <= 0, cost: 1 Second rule: l4 -> l2 : TRUE, cost: 1 New rule: l2 -> l2 : x_5^0'=-1+x_5^0, y_6^0-__const_29^0 <= 0, cost: 2 Applied deletion Removed the following rules: 10 11 Eliminated locations on linear paths Start location: l5 7: l0 -> l2 : -__const_19^0+x_5^0 <= 0, cost: 1 9: l2 -> l0 : x_5^0'=-1+x_5^0, 1-y_6^0+__const_29^0 <= 0, cost: 1 14: l2 -> l2 : x_5^0'=-1+x_5^0, y_6^0-__const_29^0 <= 0, cost: 2 13: l5 -> l0 : TRUE, cost: 2 Applied nonterm Original rule: l2 -> l2 : x_5^0'=-1+x_5^0, y_6^0-__const_29^0 <= 0, cost: 2 New rule: l2 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_CMlOlA.txt Applied deletion Removed the following rules: 14 Accelerated simple loops Start location: l5 7: l0 -> l2 : -__const_19^0+x_5^0 <= 0, cost: 1 9: l2 -> l0 : x_5^0'=-1+x_5^0, 1-y_6^0+__const_29^0 <= 0, cost: 1 15: l2 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ n >= 0), cost: NONTERM 13: l5 -> l0 : TRUE, cost: 2 Applied chaining First rule: l0 -> l2 : -__const_19^0+x_5^0 <= 0, cost: 1 Second rule: l2 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ n >= 0), cost: NONTERM New rule: l0 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ -__const_19^0+x_5^0 <= 0), cost: NONTERM Applied deletion Removed the following rules: 15 Chained accelerated rules with incoming rules Start location: l5 7: l0 -> l2 : -__const_19^0+x_5^0 <= 0, cost: 1 16: l0 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ -__const_19^0+x_5^0 <= 0), cost: NONTERM 9: l2 -> l0 : x_5^0'=-1+x_5^0, 1-y_6^0+__const_29^0 <= 0, cost: 1 13: l5 -> l0 : TRUE, cost: 2 Eliminating location l2 by chaining: Applied chaining First rule: l0 -> l2 : -__const_19^0+x_5^0 <= 0, cost: 1 Second rule: l2 -> l0 : x_5^0'=-1+x_5^0, 1-y_6^0+__const_29^0 <= 0, cost: 1 New rule: l0 -> l0 : x_5^0'=-1+x_5^0, (1-y_6^0+__const_29^0 <= 0 /\ -__const_19^0+x_5^0 <= 0), cost: 2 Applied deletion Removed the following rules: 7 9 Eliminated locations on linear paths Start location: l5 16: l0 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ -__const_19^0+x_5^0 <= 0), cost: NONTERM 17: l0 -> l0 : x_5^0'=-1+x_5^0, (1-y_6^0+__const_29^0 <= 0 /\ -__const_19^0+x_5^0 <= 0), cost: 2 13: l5 -> l0 : TRUE, cost: 2 Applied nonterm Original rule: l0 -> l0 : x_5^0'=-1+x_5^0, (1-y_6^0+__const_29^0 <= 0 /\ -__const_19^0+x_5^0 <= 0), cost: 2 New rule: l0 -> [7] : (n0 >= 0 /\ __const_19^0-x_5^0 >= 0 /\ -1+y_6^0-__const_29^0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_iiekJa.txt Applied deletion Removed the following rules: 17 Accelerated simple loops Start location: l5 16: l0 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ -__const_19^0+x_5^0 <= 0), cost: NONTERM 18: l0 -> [7] : (n0 >= 0 /\ __const_19^0-x_5^0 >= 0 /\ -1+y_6^0-__const_29^0 >= 0), cost: NONTERM 13: l5 -> l0 : TRUE, cost: 2 Applied chaining First rule: l5 -> l0 : TRUE, cost: 2 Second rule: l0 -> [7] : (n0 >= 0 /\ __const_19^0-x_5^0 >= 0 /\ -1+y_6^0-__const_29^0 >= 0), cost: NONTERM New rule: l5 -> [7] : (__const_19^0-x_5^0 >= 0 /\ -1+y_6^0-__const_29^0 >= 0), cost: NONTERM Applied deletion Removed the following rules: 18 Chained accelerated rules with incoming rules Start location: l5 16: l0 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ -__const_19^0+x_5^0 <= 0), cost: NONTERM 13: l5 -> l0 : TRUE, cost: 2 19: l5 -> [7] : (__const_19^0-x_5^0 >= 0 /\ -1+y_6^0-__const_29^0 >= 0), cost: NONTERM Eliminating location l0 by chaining: Applied chaining First rule: l5 -> l0 : TRUE, cost: 2 Second rule: l0 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ -__const_19^0+x_5^0 <= 0), cost: NONTERM New rule: l5 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ -__const_19^0+x_5^0 <= 0), cost: NONTERM Applied deletion Removed the following rules: 13 16 Eliminated locations on linear paths Start location: l5 19: l5 -> [7] : (__const_19^0-x_5^0 >= 0 /\ -1+y_6^0-__const_29^0 >= 0), cost: NONTERM 20: l5 -> [6] : (-y_6^0+__const_29^0 >= 0 /\ -__const_19^0+x_5^0 <= 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 19 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (__const_19^0-x_5^0 >= 0 /\ -1+y_6^0-__const_29^0 >= 0)