NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l3 0: l0 -> l1 : __const_200^0'=__const_200^post_1, x^0'=x^post_1, [ x^post_1==1+x^0 && 1+__const_200^0<=x^post_1 && __const_200^0==__const_200^post_1 ], cost: 1 1: l1 -> l0 : __const_200^0'=__const_200^post_2, x^0'=x^post_2, [ __const_200^0==__const_200^post_2 && x^0==x^post_2 ], cost: 1 2: l2 -> l0 : __const_200^0'=__const_200^post_3, x^0'=x^post_3, [ __const_200^0==__const_200^post_3 && x^0==x^post_3 ], cost: 1 3: l3 -> l2 : __const_200^0'=__const_200^post_4, x^0'=x^post_4, [ __const_200^0==__const_200^post_4 && x^0==x^post_4 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: l3 -> l2 : __const_200^0'=__const_200^post_4, x^0'=x^post_4, [ __const_200^0==__const_200^post_4 && x^0==x^post_4 ], cost: 1 Simplified all rules, resulting in: Start location: l3 0: l0 -> l1 : x^0'=1+x^0, [ 1+__const_200^0<=1+x^0 ], cost: 1 1: l1 -> l0 : [], cost: 1 2: l2 -> l0 : [], cost: 1 3: l3 -> l2 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l3 5: l0 -> l0 : x^0'=1+x^0, [ 1+__const_200^0<=1+x^0 ], cost: 2 4: l3 -> l0 : [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 5: l0 -> l0 : x^0'=1+x^0, [ 1+__const_200^0<=1+x^0 ], cost: 2 Accelerated rule 5 with non-termination, yielding the new rule 6. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 5. Accelerated all simple loops using metering functions (where possible): Start location: l3 6: l0 -> [4] : [ 1+__const_200^0<=1+x^0 ], cost: NONTERM 4: l3 -> l0 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l3 4: l3 -> l0 : [], cost: 2 7: l3 -> [4] : [ 1+__const_200^0<=1+x^0 ], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l3 7: l3 -> [4] : [ 1+__const_200^0<=1+x^0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l3 7: l3 -> [4] : [ 1+__const_200^0<=1+x^0 ], cost: NONTERM Computing asymptotic complexity for rule 7 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+__const_200^0<=1+x^0 ] NO