NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l9 0: l0 -> l1 : Result_4^0'=Result_4^post_1, __disjvr_0^0'=__disjvr_0^post_1, __disjvr_1^0'=__disjvr_1^post_1, tmp_6^0'=tmp_6^post_1, x_5^0'=x_5^post_1, [ Result_4^0==Result_4^post_1 && __disjvr_0^0==__disjvr_0^post_1 && __disjvr_1^0==__disjvr_1^post_1 && tmp_6^0==tmp_6^post_1 && x_5^0==x_5^post_1 ], cost: 1 1: l1 -> l2 : Result_4^0'=Result_4^post_2, __disjvr_0^0'=__disjvr_0^post_2, __disjvr_1^0'=__disjvr_1^post_2, tmp_6^0'=tmp_6^post_2, x_5^0'=x_5^post_2, [ tmp_6^post_2==tmp_6^post_2 && tmp_6^post_2<=0 && 0<=tmp_6^post_2 && x_5^0<=0 && Result_4^post_2==Result_4^post_2 && __disjvr_0^0==__disjvr_0^post_2 && __disjvr_1^0==__disjvr_1^post_2 && x_5^0==x_5^post_2 ], cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post_3, __disjvr_0^0'=__disjvr_0^post_3, __disjvr_1^0'=__disjvr_1^post_3, tmp_6^0'=tmp_6^post_3, x_5^0'=x_5^post_3, [ tmp_6^post_3==tmp_6^post_3 && tmp_6^post_3<=0 && 0<=tmp_6^post_3 && 0<=-1+x_5^0 && Result_4^0==Result_4^post_3 && __disjvr_0^0==__disjvr_0^post_3 && __disjvr_1^0==__disjvr_1^post_3 && x_5^0==x_5^post_3 ], cost: 1 4: l1 -> l4 : Result_4^0'=Result_4^post_5, __disjvr_0^0'=__disjvr_0^post_5, __disjvr_1^0'=__disjvr_1^post_5, tmp_6^0'=tmp_6^post_5, x_5^0'=x_5^post_5, [ tmp_6^post_5==tmp_6^post_5 && Result_4^0==Result_4^post_5 && __disjvr_0^0==__disjvr_0^post_5 && __disjvr_1^0==__disjvr_1^post_5 && x_5^0==x_5^post_5 ], cost: 1 7: l1 -> l7 : Result_4^0'=Result_4^post_8, __disjvr_0^0'=__disjvr_0^post_8, __disjvr_1^0'=__disjvr_1^post_8, tmp_6^0'=tmp_6^post_8, x_5^0'=x_5^post_8, [ tmp_6^post_8==tmp_6^post_8 && Result_4^0==Result_4^post_8 && __disjvr_0^0==__disjvr_0^post_8 && __disjvr_1^0==__disjvr_1^post_8 && x_5^0==x_5^post_8 ], cost: 1 3: l3 -> l1 : Result_4^0'=Result_4^post_4, __disjvr_0^0'=__disjvr_0^post_4, __disjvr_1^0'=__disjvr_1^post_4, tmp_6^0'=tmp_6^post_4, x_5^0'=x_5^post_4, [ Result_4^0==Result_4^post_4 && __disjvr_0^0==__disjvr_0^post_4 && __disjvr_1^0==__disjvr_1^post_4 && tmp_6^0==tmp_6^post_4 && x_5^0==x_5^post_4 ], cost: 1 5: l4 -> l5 : Result_4^0'=Result_4^post_6, __disjvr_0^0'=__disjvr_0^post_6, __disjvr_1^0'=__disjvr_1^post_6, tmp_6^0'=tmp_6^post_6, x_5^0'=x_5^post_6, [ __disjvr_0^post_6==__disjvr_0^0 && Result_4^0==Result_4^post_6 && __disjvr_0^0==__disjvr_0^post_6 && __disjvr_1^0==__disjvr_1^post_6 && tmp_6^0==tmp_6^post_6 && x_5^0==x_5^post_6 ], cost: 1 6: l5 -> l2 : Result_4^0'=Result_4^post_7, __disjvr_0^0'=__disjvr_0^post_7, __disjvr_1^0'=__disjvr_1^post_7, tmp_6^0'=tmp_6^post_7, x_5^0'=x_5^post_7, [ x_5^post_7==-1+x_5^0 && x_5^post_7<=0 && Result_4^post_7==Result_4^post_7 && __disjvr_0^0==__disjvr_0^post_7 && __disjvr_1^0==__disjvr_1^post_7 && tmp_6^0==tmp_6^post_7 ], cost: 1 8: l7 -> l8 : Result_4^0'=Result_4^post_9, __disjvr_0^0'=__disjvr_0^post_9, __disjvr_1^0'=__disjvr_1^post_9, tmp_6^0'=tmp_6^post_9, x_5^0'=x_5^post_9, [ __disjvr_1^post_9==__disjvr_1^0 && Result_4^0==Result_4^post_9 && __disjvr_0^0==__disjvr_0^post_9 && __disjvr_1^0==__disjvr_1^post_9 && tmp_6^0==tmp_6^post_9 && x_5^0==x_5^post_9 ], cost: 1 9: l8 -> l6 : Result_4^0'=Result_4^post_10, __disjvr_0^0'=__disjvr_0^post_10, __disjvr_1^0'=__disjvr_1^post_10, tmp_6^0'=tmp_6^post_10, x_5^0'=x_5^post_10, [ x_5^post_10==-1+x_5^0 && 0<=-1+x_5^post_10 && Result_4^0==Result_4^post_10 && __disjvr_0^0==__disjvr_0^post_10 && __disjvr_1^0==__disjvr_1^post_10 && tmp_6^0==tmp_6^post_10 ], cost: 1 10: l6 -> l1 : Result_4^0'=Result_4^post_11, __disjvr_0^0'=__disjvr_0^post_11, __disjvr_1^0'=__disjvr_1^post_11, tmp_6^0'=tmp_6^post_11, x_5^0'=x_5^post_11, [ Result_4^0==Result_4^post_11 && __disjvr_0^0==__disjvr_0^post_11 && __disjvr_1^0==__disjvr_1^post_11 && tmp_6^0==tmp_6^post_11 && x_5^0==x_5^post_11 ], cost: 1 11: l9 -> l0 : Result_4^0'=Result_4^post_12, __disjvr_0^0'=__disjvr_0^post_12, __disjvr_1^0'=__disjvr_1^post_12, tmp_6^0'=tmp_6^post_12, x_5^0'=x_5^post_12, [ Result_4^0==Result_4^post_12 && __disjvr_0^0==__disjvr_0^post_12 && __disjvr_1^0==__disjvr_1^post_12 && tmp_6^0==tmp_6^post_12 && x_5^0==x_5^post_12 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 11: l9 -> l0 : Result_4^0'=Result_4^post_12, __disjvr_0^0'=__disjvr_0^post_12, __disjvr_1^0'=__disjvr_1^post_12, tmp_6^0'=tmp_6^post_12, x_5^0'=x_5^post_12, [ Result_4^0==Result_4^post_12 && __disjvr_0^0==__disjvr_0^post_12 && __disjvr_1^0==__disjvr_1^post_12 && tmp_6^0==tmp_6^post_12 && x_5^0==x_5^post_12 ], cost: 1 Removed unreachable and leaf rules: Start location: l9 0: l0 -> l1 : Result_4^0'=Result_4^post_1, __disjvr_0^0'=__disjvr_0^post_1, __disjvr_1^0'=__disjvr_1^post_1, tmp_6^0'=tmp_6^post_1, x_5^0'=x_5^post_1, [ Result_4^0==Result_4^post_1 && __disjvr_0^0==__disjvr_0^post_1 && __disjvr_1^0==__disjvr_1^post_1 && tmp_6^0==tmp_6^post_1 && x_5^0==x_5^post_1 ], cost: 1 2: l1 -> l3 : Result_4^0'=Result_4^post_3, __disjvr_0^0'=__disjvr_0^post_3, __disjvr_1^0'=__disjvr_1^post_3, tmp_6^0'=tmp_6^post_3, x_5^0'=x_5^post_3, [ tmp_6^post_3==tmp_6^post_3 && tmp_6^post_3<=0 && 0<=tmp_6^post_3 && 0<=-1+x_5^0 && Result_4^0==Result_4^post_3 && __disjvr_0^0==__disjvr_0^post_3 && __disjvr_1^0==__disjvr_1^post_3 && x_5^0==x_5^post_3 ], cost: 1 7: l1 -> l7 : Result_4^0'=Result_4^post_8, __disjvr_0^0'=__disjvr_0^post_8, __disjvr_1^0'=__disjvr_1^post_8, tmp_6^0'=tmp_6^post_8, x_5^0'=x_5^post_8, [ tmp_6^post_8==tmp_6^post_8 && Result_4^0==Result_4^post_8 && __disjvr_0^0==__disjvr_0^post_8 && __disjvr_1^0==__disjvr_1^post_8 && x_5^0==x_5^post_8 ], cost: 1 3: l3 -> l1 : Result_4^0'=Result_4^post_4, __disjvr_0^0'=__disjvr_0^post_4, __disjvr_1^0'=__disjvr_1^post_4, tmp_6^0'=tmp_6^post_4, x_5^0'=x_5^post_4, [ Result_4^0==Result_4^post_4 && __disjvr_0^0==__disjvr_0^post_4 && __disjvr_1^0==__disjvr_1^post_4 && tmp_6^0==tmp_6^post_4 && x_5^0==x_5^post_4 ], cost: 1 8: l7 -> l8 : Result_4^0'=Result_4^post_9, __disjvr_0^0'=__disjvr_0^post_9, __disjvr_1^0'=__disjvr_1^post_9, tmp_6^0'=tmp_6^post_9, x_5^0'=x_5^post_9, [ __disjvr_1^post_9==__disjvr_1^0 && Result_4^0==Result_4^post_9 && __disjvr_0^0==__disjvr_0^post_9 && __disjvr_1^0==__disjvr_1^post_9 && tmp_6^0==tmp_6^post_9 && x_5^0==x_5^post_9 ], cost: 1 9: l8 -> l6 : Result_4^0'=Result_4^post_10, __disjvr_0^0'=__disjvr_0^post_10, __disjvr_1^0'=__disjvr_1^post_10, tmp_6^0'=tmp_6^post_10, x_5^0'=x_5^post_10, [ x_5^post_10==-1+x_5^0 && 0<=-1+x_5^post_10 && Result_4^0==Result_4^post_10 && __disjvr_0^0==__disjvr_0^post_10 && __disjvr_1^0==__disjvr_1^post_10 && tmp_6^0==tmp_6^post_10 ], cost: 1 10: l6 -> l1 : Result_4^0'=Result_4^post_11, __disjvr_0^0'=__disjvr_0^post_11, __disjvr_1^0'=__disjvr_1^post_11, tmp_6^0'=tmp_6^post_11, x_5^0'=x_5^post_11, [ Result_4^0==Result_4^post_11 && __disjvr_0^0==__disjvr_0^post_11 && __disjvr_1^0==__disjvr_1^post_11 && tmp_6^0==tmp_6^post_11 && x_5^0==x_5^post_11 ], cost: 1 11: l9 -> l0 : Result_4^0'=Result_4^post_12, __disjvr_0^0'=__disjvr_0^post_12, __disjvr_1^0'=__disjvr_1^post_12, tmp_6^0'=tmp_6^post_12, x_5^0'=x_5^post_12, [ Result_4^0==Result_4^post_12 && __disjvr_0^0==__disjvr_0^post_12 && __disjvr_1^0==__disjvr_1^post_12 && tmp_6^0==tmp_6^post_12 && x_5^0==x_5^post_12 ], cost: 1 Simplified all rules, resulting in: Start location: l9 0: l0 -> l1 : [], cost: 1 2: l1 -> l3 : tmp_6^0'=0, [ 0<=-1+x_5^0 ], cost: 1 7: l1 -> l7 : tmp_6^0'=tmp_6^post_8, [], cost: 1 3: l3 -> l1 : [], cost: 1 8: l7 -> l8 : [], cost: 1 9: l8 -> l6 : x_5^0'=-1+x_5^0, [ 0<=-2+x_5^0 ], cost: 1 10: l6 -> l1 : [], cost: 1 11: l9 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l9 13: l1 -> l1 : tmp_6^0'=0, [ 0<=-1+x_5^0 ], cost: 2 16: l1 -> l1 : tmp_6^0'=tmp_6^post_8, x_5^0'=-1+x_5^0, [ 0<=-2+x_5^0 ], cost: 4 12: l9 -> l1 : [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 13: l1 -> l1 : tmp_6^0'=0, [ 0<=-1+x_5^0 ], cost: 2 16: l1 -> l1 : tmp_6^0'=tmp_6^post_8, x_5^0'=-1+x_5^0, [ 0<=-2+x_5^0 ], cost: 4 Accelerated rule 13 with non-termination, yielding the new rule 17. Accelerated rule 16 with backward acceleration, yielding the new rule 18. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 13 16. Accelerated all simple loops using metering functions (where possible): Start location: l9 17: l1 -> [10] : [ 0<=-1+x_5^0 ], cost: NONTERM 18: l1 -> l1 : tmp_6^0'=tmp_6^post_8, x_5^0'=1, [ -1+x_5^0>=1 ], cost: -4+4*x_5^0 12: l9 -> l1 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l9 12: l9 -> l1 : [], cost: 2 19: l9 -> [10] : [ 0<=-1+x_5^0 ], cost: NONTERM 20: l9 -> l1 : tmp_6^0'=tmp_6^post_8, x_5^0'=1, [ -1+x_5^0>=1 ], cost: -2+4*x_5^0 Removed unreachable locations (and leaf rules with constant cost): Start location: l9 19: l9 -> [10] : [ 0<=-1+x_5^0 ], cost: NONTERM 20: l9 -> l1 : tmp_6^0'=tmp_6^post_8, x_5^0'=1, [ -1+x_5^0>=1 ], cost: -2+4*x_5^0 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l9 19: l9 -> [10] : [ 0<=-1+x_5^0 ], cost: NONTERM 20: l9 -> l1 : tmp_6^0'=tmp_6^post_8, x_5^0'=1, [ -1+x_5^0>=1 ], cost: -2+4*x_5^0 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