NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1 4: f3 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>=1 && arg2>=1 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1 6: f3 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1<1 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1 7: f3 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg2<1 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==2*arg1 && arg2==arg2P_3 ], cost: 1 3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==3*arg2 && arg1==arg1P_4 ], cost: 1 5: f6 -> f3 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1 8: __init -> f1 : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 8: __init -> f1 : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1 4: f3 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>=1 && arg2>=1 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3==2*arg1 && arg2==arg2P_3 ], cost: 1 3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==3*arg2 && arg1==arg1P_4 ], cost: 1 5: f6 -> f3 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1 8: __init -> f1 : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1 1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1 4: f3 -> f4 : [ arg1>=1 && arg2>=1 ], cost: 1 2: f4 -> f5 : arg1'=2*arg1, [], cost: 1 3: f5 -> f6 : arg2'=3*arg2, [], cost: 1 5: f6 -> f3 : [], cost: 1 8: __init -> f1 : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 13: f3 -> f3 : arg1'=2*arg1, arg2'=3*arg2, [ arg1>=1 && arg2>=1 ], cost: 4 10: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3 Accelerating simple loops of location 2. Accelerating the following rules: 13: f3 -> f3 : arg1'=2*arg1, arg2'=3*arg2, [ arg1>=1 && arg2>=1 ], cost: 4 Accelerated rule 13 with non-termination, yielding the new rule 14. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 13. Accelerated all simple loops using metering functions (where possible): Start location: __init 14: f3 -> [8] : [ arg1>=1 && arg2>=1 ], cost: NONTERM 10: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3 Chained accelerated rules (with incoming rules): Start location: __init 10: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3 15: __init -> [8] : [], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: __init 15: __init -> [8] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 15: __init -> [8] : [], cost: NONTERM Computing asymptotic complexity for rule 15 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