NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [ 0==arg1P_1 ], cost: 1 3: f2 -> f3 : arg1'=arg1P_4, [ arg1<100 && arg1==arg1P_4 ], cost: 1 5: f2 -> f6 : arg1'=arg1P_6, [ arg1>=100 && arg1==arg1P_6 ], cost: 1 1: f3 -> f4 : arg1'=arg1P_2, [ arg1P_2==1+arg1 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, [ arg1P_3==-1+arg1 ], cost: 1 4: f5 -> f2 : arg1'=arg1P_5, [ arg1==arg1P_5 ], cost: 1 6: __init -> f1 : arg1'=arg1P_7, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: __init -> f1 : arg1'=arg1P_7, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, [ 0==arg1P_1 ], cost: 1 3: f2 -> f3 : arg1'=arg1P_4, [ arg1<100 && arg1==arg1P_4 ], cost: 1 1: f3 -> f4 : arg1'=arg1P_2, [ arg1P_2==1+arg1 ], cost: 1 2: f4 -> f5 : arg1'=arg1P_3, [ arg1P_3==-1+arg1 ], cost: 1 4: f5 -> f2 : arg1'=arg1P_5, [ arg1==arg1P_5 ], cost: 1 6: __init -> f1 : arg1'=arg1P_7, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=0, [], cost: 1 3: f2 -> f3 : [ arg1<100 ], cost: 1 1: f3 -> f4 : arg1'=1+arg1, [], cost: 1 2: f4 -> f5 : arg1'=-1+arg1, [], cost: 1 4: f5 -> f2 : [], cost: 1 6: __init -> f1 : arg1'=arg1P_7, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 10: f2 -> f2 : arg1'=arg1, [ arg1<100 ], cost: 4 7: __init -> f2 : arg1'=0, [], cost: 2 Accelerating simple loops of location 1. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 10: f2 -> f2 : [ arg1<100 ], cost: 4 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: __init 11: f2 -> [7] : [ arg1<100 ], cost: NONTERM 7: __init -> f2 : arg1'=0, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 7: __init -> f2 : arg1'=0, [], cost: 2 12: __init -> [7] : [], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: __init 12: __init -> [7] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 12: __init -> [7] : [], cost: NONTERM Computing asymptotic complexity for rule 12 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