WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_ConstantStackPush -> f375_0_dif_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ 0==arg1P_1 && 0==arg2P_1 && 0==arg3P_1 ], cost: 1 1: f375_0_dif_GE -> f484_0_dif_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg2<20 && arg2==arg3 && arg1==arg1P_2 && arg2==arg2P_2 && 0==arg3P_2 && 0==arg4P_2 && 0==arg5P_2 ], cost: 1 2: f484_0_dif_GE -> f375_0_dif_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg4>19 && 1==arg3 && arg4==arg5 && arg1==arg1P_3 && 1+arg2==arg2P_3 && 1+arg2==arg3P_3 ], cost: 1 3: f484_0_dif_GE -> f375_0_dif_GE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg4<20 && 1==arg3 && arg4==arg5 && arg1==arg1P_4 && 1+arg2==arg2P_4 && 1+arg2==arg3P_4 ], cost: 1 4: f484_0_dif_GE -> f484_0_dif_GE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2<20 && x29_1>x30_1 && arg4<20 && 0==arg3 && arg4==arg5 && arg1==arg1P_5 && arg2==arg2P_5 && 0==arg3P_5 && 1+arg4==arg4P_5 && 1+arg4==arg5P_5 ], cost: 1 5: f484_0_dif_GE -> f484_0_dif_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg2<20 && x36_1 f375_0_dif_GE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1<20 && arg2<20 && arg4>19 && 0==arg3 && arg4==arg5 && 1+arg1==arg1P_7 && 1+arg2==arg2P_7 && 1+arg2==arg3P_7 ], cost: 1 7: f484_0_dif_GE -> f484_0_dif_GE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg4<20 && arg2<20 && 0==arg3 && arg4==arg5 && arg1==arg1P_8 && arg2==arg2P_8 && 1==arg3P_8 && arg4==arg4P_8 && arg4==arg5P_8 ], cost: 1 8: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 8: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_ConstantStackPush -> f375_0_dif_GE : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [], cost: 1 1: f375_0_dif_GE -> f484_0_dif_GE : arg3'=0, arg4'=0, arg5'=0, [ arg2<20 && arg2==arg3 ], cost: 1 2: f484_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_3, arg5'=arg5P_3, [ arg4>19 && 1==arg3 && arg4==arg5 ], cost: 1 3: f484_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_4, arg5'=arg5P_4, [ arg4<20 && 1==arg3 && arg4==arg5 ], cost: 1 5: f484_0_dif_GE -> f484_0_dif_GE : arg3'=0, arg4'=1+arg4, arg5'=1+arg4, [ arg2<20 && arg4<20 && 0==arg3 && arg4==arg5 ], cost: 1 6: f484_0_dif_GE -> f375_0_dif_GE : arg1'=1+arg1, arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1<20 && arg2<20 && arg4>19 && 0==arg3 && arg4==arg5 ], cost: 1 7: f484_0_dif_GE -> f484_0_dif_GE : arg3'=1, arg5'=arg4, [ arg4<20 && arg2<20 && 0==arg3 && arg4==arg5 ], cost: 1 8: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 5: f484_0_dif_GE -> f484_0_dif_GE : arg3'=0, arg4'=1+arg4, arg5'=1+arg4, [ arg2<20 && arg4<20 && 0==arg3 && arg4==arg5 ], cost: 1 7: f484_0_dif_GE -> f484_0_dif_GE : arg3'=1, arg5'=arg4, [ arg4<20 && arg2<20 && 0==arg3 && arg4==arg5 ], cost: 1 Accelerated rule 5 with backward acceleration, yielding the new rule 9. Failed to prove monotonicity of the guard of rule 7. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 5. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_ConstantStackPush -> f375_0_dif_GE : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [], cost: 1 1: f375_0_dif_GE -> f484_0_dif_GE : arg3'=0, arg4'=0, arg5'=0, [ arg2<20 && arg2==arg3 ], cost: 1 2: f484_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_3, arg5'=arg5P_3, [ arg4>19 && 1==arg3 && arg4==arg5 ], cost: 1 3: f484_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_4, arg5'=arg5P_4, [ arg4<20 && 1==arg3 && arg4==arg5 ], cost: 1 6: f484_0_dif_GE -> f375_0_dif_GE : arg1'=1+arg1, arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1<20 && arg2<20 && arg4>19 && 0==arg3 && arg4==arg5 ], cost: 1 7: f484_0_dif_GE -> f484_0_dif_GE : arg3'=1, arg5'=arg4, [ arg4<20 && arg2<20 && 0==arg3 && arg4==arg5 ], cost: 1 9: f484_0_dif_GE -> f484_0_dif_GE : arg3'=0, arg4'=20, arg5'=20, [ arg2<20 && 0==arg3 && arg4==arg5 && 20-arg4>=1 ], cost: 20-arg4 8: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_ConstantStackPush -> f375_0_dif_GE : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [], cost: 1 1: f375_0_dif_GE -> f484_0_dif_GE : arg3'=0, arg4'=0, arg5'=0, [ arg2<20 && arg2==arg3 ], cost: 1 10: f375_0_dif_GE -> f484_0_dif_GE : arg3'=1, arg4'=0, arg5'=0, [ arg2<20 && arg2==arg3 ], cost: 2 11: f375_0_dif_GE -> f484_0_dif_GE : arg3'=0, arg4'=20, arg5'=20, [ arg2<20 && arg2==arg3 ], cost: 21 2: f484_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_3, arg5'=arg5P_3, [ arg4>19 && 1==arg3 && arg4==arg5 ], cost: 1 3: f484_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_4, arg5'=arg5P_4, [ arg4<20 && 1==arg3 && arg4==arg5 ], cost: 1 6: f484_0_dif_GE -> f375_0_dif_GE : arg1'=1+arg1, arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1<20 && arg2<20 && arg4>19 && 0==arg3 && arg4==arg5 ], cost: 1 8: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 1: f375_0_dif_GE -> f484_0_dif_GE : arg3'=0, arg4'=0, arg5'=0, [ arg2<20 && arg2==arg3 ], cost: 1 10: f375_0_dif_GE -> f484_0_dif_GE : arg3'=1, arg4'=0, arg5'=0, [ arg2<20 && arg2==arg3 ], cost: 2 11: f375_0_dif_GE -> f484_0_dif_GE : arg3'=0, arg4'=20, arg5'=20, [ arg2<20 && arg2==arg3 ], cost: 21 2: f484_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_3, arg5'=arg5P_3, [ arg4>19 && 1==arg3 && arg4==arg5 ], cost: 1 3: f484_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_4, arg5'=arg5P_4, [ arg4<20 && 1==arg3 && arg4==arg5 ], cost: 1 6: f484_0_dif_GE -> f375_0_dif_GE : arg1'=1+arg1, arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1<20 && arg2<20 && arg4>19 && 0==arg3 && arg4==arg5 ], cost: 1 12: __init -> f375_0_dif_GE : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 13: f375_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_4, arg5'=arg5P_4, [ arg2<20 && arg2==arg3 ], cost: 3 14: f375_0_dif_GE -> f375_0_dif_GE : arg1'=1+arg1, arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_7, arg5'=arg5P_7, [ arg2<20 && arg2==arg3 && arg1<20 ], cost: 22 12: __init -> f375_0_dif_GE : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 13: f375_0_dif_GE -> f375_0_dif_GE : arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_4, arg5'=arg5P_4, [ arg2<20 && arg2==arg3 ], cost: 3 14: f375_0_dif_GE -> f375_0_dif_GE : arg1'=1+arg1, arg2'=1+arg2, arg3'=1+arg2, arg4'=arg4P_7, arg5'=arg5P_7, [ arg2<20 && arg2==arg3 && arg1<20 ], cost: 22 Accelerated rule 13 with backward acceleration, yielding the new rule 15. Accelerated rule 14 with backward acceleration, yielding the new rule 16. Accelerated rule 14 with backward acceleration, yielding the new rule 17. [accelerate] Nesting with 3 inner and 2 outer candidates Removing the simple loops: 13 14. Accelerated all simple loops using metering functions (where possible): Start location: __init 15: f375_0_dif_GE -> f375_0_dif_GE : arg2'=20, arg3'=20, arg4'=arg4P_4, arg5'=arg5P_4, [ arg2==arg3 && 20-arg2>=1 ], cost: 60-3*arg2 16: f375_0_dif_GE -> f375_0_dif_GE : arg1'=20-arg2+arg1, arg2'=20, arg3'=20, arg4'=arg4P_7, arg5'=arg5P_7, [ arg2==arg3 && 20-arg2>=1 && 19-arg2+arg1<20 ], cost: 440-22*arg2 17: f375_0_dif_GE -> f375_0_dif_GE : arg1'=20, arg2'=20+arg2-arg1, arg3'=20+arg2-arg1, arg4'=arg4P_7, arg5'=arg5P_7, [ arg2==arg3 && 20-arg1>=1 && 19+arg2-arg1<20 ], cost: 440-22*arg1 12: __init -> f375_0_dif_GE : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 12: __init -> f375_0_dif_GE : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [], cost: 2 18: __init -> f375_0_dif_GE : arg1'=0, arg2'=20, arg3'=20, arg4'=arg4P_4, arg5'=arg5P_4, [], cost: 62 19: __init -> f375_0_dif_GE : arg1'=20, arg2'=20, arg3'=20, arg4'=arg4P_7, arg5'=arg5P_7, [], cost: 442 20: __init -> f375_0_dif_GE : arg1'=20, arg2'=20, arg3'=20, arg4'=arg4P_7, arg5'=arg5P_7, [], cost: 442 Removed unreachable locations (and leaf rules with constant cost): Start location: __init ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [] WORST_CASE(Omega(1),?)