NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l5 0: l0 -> l1 : Result_4^0'=Result_4^post_1, x_5^0'=x_5^post_1, [ Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 ], cost: 1 1: l1 -> l2 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, [ -x_5^0<=0 && x_5^0<=0 && Result_4^post_2==Result_4^post_2 && x_5^0==x_5^post_2 ], cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ -x_5^0<=0 && 0<=-1+x_5^0 && x_5^1_1==x_5^1_1 && x_5^post_3==2+x_5^1_1 && Result_4^0==Result_4^post_3 ], cost: 1 4: l1 -> l4 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ 0<=-1-x_5^0 && x_5^1_2==x_5^1_2 && x_5^post_5==-2+x_5^1_2 && Result_4^0==Result_4^post_5 ], cost: 1 3: l3 -> l1 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 ], cost: 1 5: l4 -> l1 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, [ Result_4^0==Result_4^post_6 && x_5^0==x_5^post_6 ], cost: 1 6: l5 -> l0 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, [ Result_4^0==Result_4^post_7 && x_5^0==x_5^post_7 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: l5 -> l0 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, [ Result_4^0==Result_4^post_7 && x_5^0==x_5^post_7 ], cost: 1 Removed unreachable and leaf rules: Start location: l5 0: l0 -> l1 : Result_4^0'=Result_4^post_1, x_5^0'=x_5^post_1, [ Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 ], cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ -x_5^0<=0 && 0<=-1+x_5^0 && x_5^1_1==x_5^1_1 && x_5^post_3==2+x_5^1_1 && Result_4^0==Result_4^post_3 ], cost: 1 4: l1 -> l4 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ 0<=-1-x_5^0 && x_5^1_2==x_5^1_2 && x_5^post_5==-2+x_5^1_2 && Result_4^0==Result_4^post_5 ], cost: 1 3: l3 -> l1 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 ], cost: 1 5: l4 -> l1 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, [ Result_4^0==Result_4^post_6 && x_5^0==x_5^post_6 ], cost: 1 6: l5 -> l0 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, [ Result_4^0==Result_4^post_7 && x_5^0==x_5^post_7 ], cost: 1 Simplified all rules, resulting in: Start location: l5 0: l0 -> l1 : [], cost: 1 2: l1 -> l3 : x_5^0'=2+x_5^1_1, [ 0<=-1+x_5^0 ], cost: 1 4: l1 -> l4 : x_5^0'=-2+x_5^1_2, [ 0<=-1-x_5^0 ], cost: 1 3: l3 -> l1 : [], cost: 1 5: l4 -> l1 : [], cost: 1 6: l5 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l5 8: l1 -> l1 : x_5^0'=2+x_5^1_1, [ 0<=-1+x_5^0 ], cost: 2 9: l1 -> l1 : x_5^0'=-2+x_5^1_2, [ 0<=-1-x_5^0 ], cost: 2 7: l5 -> l1 : [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 8: l1 -> l1 : x_5^0'=2+x_5^1_1, [ 0<=-1+x_5^0 ], cost: 2 9: l1 -> l1 : x_5^0'=-2+x_5^1_2, [ 0<=-1-x_5^0 ], cost: 2 [test] deduced pseudo-invariant -1-x_5^1_1<=0, also trying 1+x_5^1_1<=-1 Accelerated rule 8 with non-termination, yielding the new rule 10. Accelerated rule 8 with non-termination, yielding the new rule 11. Accelerated rule 8 with backward acceleration, yielding the new rule 12. [test] deduced pseudo-invariant -2-x_5^0+x_5^1_2<=0, also trying 2+x_5^0-x_5^1_2<=-1 Accelerated rule 9 with non-termination, yielding the new rule 13. Accelerated rule 9 with non-termination, yielding the new rule 14. Accelerated rule 9 with backward acceleration, yielding the new rule 15. [accelerate] Nesting with 0 inner and 2 outer candidates Also removing duplicate rules: 11 14. Accelerated all simple loops using metering functions (where possible): Start location: l5 8: l1 -> l1 : x_5^0'=2+x_5^1_1, [ 0<=-1+x_5^0 ], cost: 2 9: l1 -> l1 : x_5^0'=-2+x_5^1_2, [ 0<=-1-x_5^0 ], cost: 2 10: l1 -> [6] : [ 0<=-1+x_5^0 && 0<=1+x_5^1_1 ], cost: NONTERM 12: l1 -> [6] : [ 0<=-1+x_5^0 && -1-x_5^1_1<=0 ], cost: NONTERM 13: l1 -> [6] : [ 0<=-1-x_5^0 && 0<=1-x_5^1_2 ], cost: NONTERM 15: l1 -> [6] : [ 0<=-1-x_5^0 && -2-x_5^0+x_5^1_2<=0 ], cost: NONTERM 7: l5 -> l1 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l5 7: l5 -> l1 : [], cost: 2 16: l5 -> l1 : x_5^0'=2+x_5^1_1, [ 0<=-1+x_5^0 ], cost: 4 17: l5 -> l1 : x_5^0'=-2+x_5^1_2, [ 0<=-1-x_5^0 ], cost: 4 18: l5 -> [6] : [ 0<=-1+x_5^0 ], cost: NONTERM 19: l5 -> [6] : [ 0<=-1+x_5^0 ], cost: NONTERM 20: l5 -> [6] : [ 0<=-1-x_5^0 ], cost: NONTERM 21: l5 -> [6] : [ 0<=-1-x_5^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l5 18: l5 -> [6] : [ 0<=-1+x_5^0 ], cost: NONTERM 19: l5 -> [6] : [ 0<=-1+x_5^0 ], cost: NONTERM 20: l5 -> [6] : [ 0<=-1-x_5^0 ], cost: NONTERM 21: l5 -> [6] : [ 0<=-1-x_5^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l5 19: l5 -> [6] : [ 0<=-1+x_5^0 ], cost: NONTERM 21: l5 -> [6] : [ 0<=-1-x_5^0 ], cost: NONTERM Computing asymptotic complexity for rule 19 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [ 0<=-1+x_5^0 ] NO