NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ 0==arg1P_1 && arg2==arg2P_1 ], cost: 1 7: f2 -> f3 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1<100 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1 9: f2 -> f9 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1>=100 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1 1: f3 -> f4 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 && 0==arg2P_2 ], cost: 1 3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2<1 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1 5: f4 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2>=1 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1 2: f5 -> f6 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==arg2 && arg1==arg1P_3 ], cost: 1 4: f6 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1 6: f7 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1P_7==1+arg1 && arg2==arg2P_7 ], cost: 1 8: f8 -> f2 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1 10: __init -> f1 : arg1'=arg1P_11, arg2'=arg2P_11, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 10: __init -> f1 : arg1'=arg1P_11, arg2'=arg2P_11, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ 0==arg1P_1 && arg2==arg2P_1 ], cost: 1 7: f2 -> f3 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1<100 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1 1: f3 -> f4 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 && 0==arg2P_2 ], cost: 1 3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2<1 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1 5: f4 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2>=1 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1 2: f5 -> f6 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==arg2 && arg1==arg1P_3 ], cost: 1 4: f6 -> f4 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1 6: f7 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1P_7==1+arg1 && arg2==arg2P_7 ], cost: 1 8: f8 -> f2 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1 10: __init -> f1 : arg1'=arg1P_11, arg2'=arg2P_11, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1 -> f2 : arg1'=0, [], cost: 1 7: f2 -> f3 : [ arg1<100 ], cost: 1 1: f3 -> f4 : arg2'=0, [], cost: 1 3: f4 -> f5 : [ arg2<1 ], cost: 1 5: f4 -> f7 : [ arg2>=1 ], cost: 1 2: f5 -> f6 : [], cost: 1 4: f6 -> f4 : [], cost: 1 6: f7 -> f8 : arg1'=1+arg1, [], cost: 1 8: f8 -> f2 : [], cost: 1 10: __init -> f1 : arg1'=arg1P_11, arg2'=arg2P_11, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 12: f2 -> f4 : arg2'=0, [ arg1<100 ], cost: 2 15: f4 -> f4 : [ arg2<1 ], cost: 3 16: f4 -> f2 : arg1'=1+arg1, [ arg2>=1 ], cost: 3 11: __init -> f2 : arg1'=0, arg2'=arg2P_11, [], cost: 2 Accelerating simple loops of location 3. Accelerating the following rules: 15: f4 -> f4 : [ arg2<1 ], cost: 3 Accelerated rule 15 with non-termination, yielding the new rule 17. [accelerate] Nesting with 0 inner and 0 outer candidates Removing the simple loops: 15. Accelerated all simple loops using metering functions (where possible): Start location: __init 12: f2 -> f4 : arg2'=0, [ arg1<100 ], cost: 2 16: f4 -> f2 : arg1'=1+arg1, [ arg2>=1 ], cost: 3 17: f4 -> [10] : [ arg2<1 ], cost: NONTERM 11: __init -> f2 : arg1'=0, arg2'=arg2P_11, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 12: f2 -> f4 : arg2'=0, [ arg1<100 ], cost: 2 18: f2 -> [10] : [ arg1<100 ], cost: NONTERM 16: f4 -> f2 : arg1'=1+arg1, [ arg2>=1 ], cost: 3 11: __init -> f2 : arg1'=0, arg2'=arg2P_11, [], cost: 2 Eliminated locations (on linear paths): Start location: __init 18: f2 -> [10] : [ arg1<100 ], cost: NONTERM 11: __init -> f2 : arg1'=0, arg2'=arg2P_11, [], cost: 2 Eliminated locations (on linear paths): Start location: __init 19: __init -> [10] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 19: __init -> [10] : [], cost: NONTERM Computing asymptotic complexity for rule 19 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