NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l4 0: l0 -> l1 : [ 0<=0 ], cost: 1 2: l0 -> l2 : [ 0<=0 ], cost: 1 1: l1 -> l0 : [ 0<=0 ], cost: 1 3: l2 -> l0 : [ 0<=0 ], cost: 1 4: l3 -> l2 : [ 0<=0 ], cost: 1 5: l4 -> l3 : [ 0<=0 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 5: l4 -> l3 : [ 0<=0 ], cost: 1 Simplified all rules, resulting in: Start location: l4 0: l0 -> l1 : [], cost: 1 2: l0 -> l2 : [], cost: 1 1: l1 -> l0 : [], cost: 1 3: l2 -> l0 : [], cost: 1 4: l3 -> l2 : [], cost: 1 5: l4 -> l3 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l4 2: l0 -> l2 : [], cost: 1 7: l0 -> l0 : [], cost: 2 3: l2 -> l0 : [], cost: 1 6: l4 -> l2 : [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 7: l0 -> l0 : [], cost: 2 Accelerated rule 7 with non-termination, yielding the new rule 8. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 7. Accelerated all simple loops using metering functions (where possible): Start location: l4 2: l0 -> l2 : [], cost: 1 8: l0 -> [5] : [], cost: NONTERM 3: l2 -> l0 : [], cost: 1 6: l4 -> l2 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l4 2: l0 -> l2 : [], cost: 1 3: l2 -> l0 : [], cost: 1 9: l2 -> [5] : [], cost: NONTERM 6: l4 -> l2 : [], cost: 2 Eliminated locations (on linear paths): Start location: l4 9: l2 -> [5] : [], cost: NONTERM 10: l2 -> l2 : [], cost: 2 6: l4 -> l2 : [], cost: 2 Accelerating simple loops of location 2. Accelerating the following rules: 10: l2 -> l2 : [], cost: 2 Accelerated rule 10 with non-termination, yielding the new rule 11. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 10. Accelerated all simple loops using metering functions (where possible): Start location: l4 9: l2 -> [5] : [], cost: NONTERM 11: l2 -> [6] : [], cost: NONTERM 6: l4 -> l2 : [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l4 9: l2 -> [5] : [], cost: NONTERM 6: l4 -> l2 : [], cost: 2 12: l4 -> [6] : [], cost: NONTERM Eliminated locations (on linear paths): Start location: l4 12: l4 -> [6] : [], cost: NONTERM 13: l4 -> [5] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l4 13: l4 -> [5] : [], cost: NONTERM Computing asymptotic complexity for rule 13 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: [] NO