NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l4 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^post_2==-1+x_5^0 && x_5^post_2<=0 && Result_4^0==Result_4^post_2 ], cost: 1 3: l1 -> l3 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ x_5^post_4==-1+x_5^0 && 0<=-1+x_5^post_4 && Result_4^post_4==Result_4^post_4 ], cost: 1 2: l2 -> l1 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 ], cost: 1 4: l4 -> l0 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: l4 -> l0 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1 Removed unreachable and leaf rules: Start location: l4 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^post_2==-1+x_5^0 && x_5^post_2<=0 && Result_4^0==Result_4^post_2 ], cost: 1 2: l2 -> l1 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 ], cost: 1 4: l4 -> l0 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1 Simplified all rules, resulting in: Start location: l4 0: l0 -> l1 : [], cost: 1 1: l1 -> l2 : x_5^0'=-1+x_5^0, [ -1+x_5^0<=0 ], cost: 1 2: l2 -> l1 : [], cost: 1 4: l4 -> l0 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l4 6: l1 -> l1 : x_5^0'=-1+x_5^0, [ -1+x_5^0<=0 ], cost: 2 5: l4 -> l1 : [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 6: l1 -> l1 : x_5^0'=-1+x_5^0, [ -1+x_5^0<=0 ], cost: 2 Accelerated rule 6 with non-termination, yielding the new rule 7. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 6. Accelerated all simple loops using metering functions (where possible): Start location: l4 7: l1 -> [5] : [ -1+x_5^0<=0 ], cost: NONTERM 5: l4 -> l1 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l4 5: l4 -> l1 : [], cost: 2 8: l4 -> [5] : [ -1+x_5^0<=0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l4 8: l4 -> [5] : [ -1+x_5^0<=0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l4 8: l4 -> [5] : [ -1+x_5^0<=0 ], cost: NONTERM Computing asymptotic complexity for rule 8 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: [ -1+x_5^0<=0 ] NO