NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg4==arg4P_3 ], cost: 1 7: f4 -> f5 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2-arg3>=1 && arg1==arg3 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1 9: f4 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg2-arg3<1 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1 10: f4 -> f10 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg1 f10 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1>arg3 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1 3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1 4: f6 -> f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1==arg1P_5 && 10==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 5: f7 -> f8 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3P_6==1+arg3+arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg4==arg4P_6 ], cost: 1 6: f8 -> f9 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1 8: f9 -> f4 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1 12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2==arg2P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1 1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg3==arg3P_2 && arg4==arg4P_2 ], cost: 1 2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg4==arg4P_3 ], cost: 1 7: f4 -> f5 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2-arg3>=1 && arg1==arg3 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1 3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1 4: f6 -> f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1==arg1P_5 && 10==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 5: f7 -> f8 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3P_6==1+arg3+arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg4==arg4P_6 ], cost: 1 6: f8 -> f9 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1 8: f9 -> f4 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1 12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], 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 2: f3 -> f4 : arg3'=arg3P_3, [], cost: 1 7: f4 -> f5 : [ arg2-arg3>=1 && arg1==arg3 ], cost: 1 3: f5 -> f6 : arg4'=arg4P_4, [], cost: 1 4: f6 -> f7 : arg2'=10, [], cost: 1 5: f7 -> f8 : arg3'=1+arg3+arg4, [], cost: 1 6: f8 -> f9 : arg1'=arg3, [], cost: 1 8: f9 -> f4 : [], cost: 1 12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 20: f4 -> f4 : arg1'=1+arg4P_4+arg3, arg2'=10, arg3'=1+arg4P_4+arg3, arg4'=arg4P_4, [ arg2-arg3>=1 && arg1==arg3 ], cost: 6 15: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_13, [], cost: 4 Accelerating simple loops of location 3. Accelerating the following rules: 20: f4 -> f4 : arg1'=1+arg4P_4+arg3, arg2'=10, arg3'=1+arg4P_4+arg3, arg4'=arg4P_4, [ arg2-arg3>=1 && arg1==arg3 ], cost: 6 Accelerated rule 20 with non-termination, yielding the new rule 21. [accelerate] Nesting with 0 inner and 1 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 20: f4 -> f4 : arg1'=1+arg4P_4+arg3, arg2'=10, arg3'=1+arg4P_4+arg3, arg4'=arg4P_4, [ arg2-arg3>=1 && arg1==arg3 ], cost: 6 21: f4 -> [11] : [ arg2-arg3>=1 && arg1==arg3 && arg4P_4==-1 && arg2==10 && arg3==9 && arg1==9 ], cost: NONTERM 15: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_13, [], cost: 4 Chained accelerated rules (with incoming rules): Start location: __init 15: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, arg4'=arg4P_13, [], cost: 4 22: __init -> f4 : arg1'=1+arg4P_4+arg1P_1, arg2'=10, arg3'=1+arg4P_4+arg1P_1, arg4'=arg4P_4, [], cost: 10 23: __init -> [11] : [], cost: NONTERM Removed unreachable locations (and leaf rules with constant cost): Start location: __init 23: __init -> [11] : [], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 23: __init -> [11] : [], cost: NONTERM Computing asymptotic complexity for rule 23 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