NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l5 0: l0 -> l1 : pc_Loop^0'=pc_Loop^post_1, [ pc_Loop^post_1==2 ], cost: 1 1: l1 -> l0 : pc_Loop^0'=pc_Loop^post_2, [ pc_Loop^0==pc_Loop^post_2 ], cost: 1 2: l2 -> l3 : pc_Loop^0'=pc_Loop^post_3, [ pc_Loop^1_1==3 && pc_Loop^post_3==2 ], cost: 1 3: l3 -> l2 : pc_Loop^0'=pc_Loop^post_4, [ pc_Loop^0==pc_Loop^post_4 ], cost: 1 4: l4 -> l2 : pc_Loop^0'=pc_Loop^post_5, [ pc_Loop^post_5==2 ], cost: 1 5: l5 -> l4 : pc_Loop^0'=pc_Loop^post_6, [ pc_Loop^0==pc_Loop^post_6 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 5: l5 -> l4 : pc_Loop^0'=pc_Loop^post_6, [ pc_Loop^0==pc_Loop^post_6 ], cost: 1 Removed unreachable and leaf rules: Start location: l5 2: l2 -> l3 : pc_Loop^0'=pc_Loop^post_3, [ pc_Loop^1_1==3 && pc_Loop^post_3==2 ], cost: 1 3: l3 -> l2 : pc_Loop^0'=pc_Loop^post_4, [ pc_Loop^0==pc_Loop^post_4 ], cost: 1 4: l4 -> l2 : pc_Loop^0'=pc_Loop^post_5, [ pc_Loop^post_5==2 ], cost: 1 5: l5 -> l4 : pc_Loop^0'=pc_Loop^post_6, [ pc_Loop^0==pc_Loop^post_6 ], cost: 1 Simplified all rules, resulting in: Start location: l5 2: l2 -> l3 : pc_Loop^0'=2, [], cost: 1 3: l3 -> l2 : [], cost: 1 4: l4 -> l2 : pc_Loop^0'=2, [], cost: 1 5: l5 -> l4 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l5 7: l2 -> l2 : pc_Loop^0'=2, [], cost: 2 6: l5 -> l2 : pc_Loop^0'=2, [], cost: 2 Accelerating simple loops of location 2. Accelerating the following rules: 7: l2 -> l2 : pc_Loop^0'=2, [], 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: l5 8: l2 -> [6] : [], cost: NONTERM 6: l5 -> l2 : pc_Loop^0'=2, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l5 6: l5 -> l2 : pc_Loop^0'=2, [], cost: 2 9: l5 -> [6] : [], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: l5 9: l5 -> [6] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l5 9: l5 -> [6] : [], cost: NONTERM Computing asymptotic complexity for rule 9 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