WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f169_0_createList_Return -> f236_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1<=arg1 && -1+arg1P_1<=arg2 && arg2P_1<=arg2 && arg1>0 && arg2>-1 && arg1P_1>0 && arg2P_1>-1 ], cost: 1 4: f236_0_main_InvokeMethod -> f358_0_duplicate_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_5<=arg2 && x13_1>0 && arg3P_5<=arg2 && arg1>0 && arg2>-1 && arg1P_5>-1 && arg3P_5>-1 && 1==arg2P_5 ], cost: 1 1: f1_0_main_Load -> f236_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>-1 ], cost: 1 2: f1_0_main_Load -> f208_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 3: f208_0_createList_LE -> f208_0_createList_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 && -1+arg1==arg1P_4 ], cost: 1 5: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ 1+arg1P_6<=arg1 && 1+arg1P_6<=arg3 && 1+arg3P_6<=arg1 && 1+arg3P_6<=arg3 && arg1>0 && arg3>0 && arg1P_6>-1 && arg3P_6>-1 && 0==arg2 && 1==arg2P_6 ], cost: 1 6: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1P_7<=arg1 && arg1P_7<=arg3 && arg3P_7<=arg1 && arg3P_7<=arg3 && arg1>0 && arg3>0 && arg1P_7>0 && arg3P_7>0 && 1==arg2 && 0==arg2P_7 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 4: f236_0_main_InvokeMethod -> f358_0_duplicate_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_5<=arg2 && x13_1>0 && arg3P_5<=arg2 && arg1>0 && arg2>-1 && arg1P_5>-1 && arg3P_5>-1 && 1==arg2P_5 ], cost: 1 1: f1_0_main_Load -> f236_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>-1 ], cost: 1 2: f1_0_main_Load -> f208_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 3: f208_0_createList_LE -> f208_0_createList_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 && -1+arg1==arg1P_4 ], cost: 1 5: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ 1+arg1P_6<=arg1 && 1+arg1P_6<=arg3 && 1+arg3P_6<=arg1 && 1+arg3P_6<=arg3 && arg1>0 && arg3>0 && arg1P_6>-1 && arg3P_6>-1 && 0==arg2 && 1==arg2P_6 ], cost: 1 6: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1P_7<=arg1 && arg1P_7<=arg3 && arg3P_7<=arg1 && arg3P_7<=arg3 && arg1>0 && arg3>0 && arg1P_7>0 && arg3P_7>0 && 1==arg2 && 0==arg2P_7 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Simplified all rules, resulting in: Start location: __init 4: f236_0_main_InvokeMethod -> f358_0_duplicate_NULL : arg1'=arg1P_5, arg2'=1, arg3'=arg3P_5, [ arg1P_5<=arg2 && arg3P_5<=arg2 && arg1>0 && arg2>-1 && arg1P_5>-1 && arg3P_5>-1 ], cost: 1 1: f1_0_main_Load -> f236_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>-1 ], cost: 1 2: f1_0_main_Load -> f208_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 3: f208_0_createList_LE -> f208_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 ], cost: 1 5: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_6, arg2'=1, arg3'=arg3P_6, [ 1+arg1P_6<=arg1 && 1+arg1P_6<=arg3 && 1+arg3P_6<=arg1 && 1+arg3P_6<=arg3 && arg1>0 && arg3>0 && arg1P_6>-1 && arg3P_6>-1 && 0==arg2 ], cost: 1 6: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_7, arg2'=0, arg3'=arg3P_7, [ arg1P_7<=arg1 && arg1P_7<=arg3 && arg3P_7<=arg1 && arg3P_7<=arg3 && arg1>0 && arg3>0 && arg1P_7>0 && arg3P_7>0 && 1==arg2 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 3. Accelerating the following rules: 3: f208_0_createList_LE -> f208_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 ], cost: 1 Accelerated rule 3 with backward acceleration, yielding the new rule 8. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 3. Accelerating simple loops of location 4. Accelerating the following rules: 5: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_6, arg2'=1, arg3'=arg3P_6, [ 1+arg1P_6<=arg1 && 1+arg1P_6<=arg3 && 1+arg3P_6<=arg1 && 1+arg3P_6<=arg3 && arg1>0 && arg3>0 && arg1P_6>-1 && arg3P_6>-1 && 0==arg2 ], cost: 1 6: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_7, arg2'=0, arg3'=arg3P_7, [ arg1P_7<=arg1 && arg1P_7<=arg3 && arg3P_7<=arg1 && arg3P_7<=arg3 && arg1>0 && arg3>0 && arg1P_7>0 && arg3P_7>0 && 1==arg2 ], cost: 1 Failed to prove monotonicity of the guard of rule 5. Failed to prove monotonicity of the guard of rule 6. [accelerate] Nesting with 2 inner and 2 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 4: f236_0_main_InvokeMethod -> f358_0_duplicate_NULL : arg1'=arg1P_5, arg2'=1, arg3'=arg3P_5, [ arg1P_5<=arg2 && arg3P_5<=arg2 && arg1>0 && arg2>-1 && arg1P_5>-1 && arg3P_5>-1 ], cost: 1 1: f1_0_main_Load -> f236_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>-1 ], cost: 1 2: f1_0_main_Load -> f208_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 8: f208_0_createList_LE -> f208_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>=1 ], cost: arg1 5: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_6, arg2'=1, arg3'=arg3P_6, [ 1+arg1P_6<=arg1 && 1+arg1P_6<=arg3 && 1+arg3P_6<=arg1 && 1+arg3P_6<=arg3 && arg1>0 && arg3>0 && arg1P_6>-1 && arg3P_6>-1 && 0==arg2 ], cost: 1 6: f358_0_duplicate_NULL -> f358_0_duplicate_NULL : arg1'=arg1P_7, arg2'=0, arg3'=arg3P_7, [ arg1P_7<=arg1 && arg1P_7<=arg3 && arg3P_7<=arg1 && arg3P_7<=arg3 && arg1>0 && arg3>0 && arg1P_7>0 && arg3P_7>0 && 1==arg2 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 4: f236_0_main_InvokeMethod -> f358_0_duplicate_NULL : arg1'=arg1P_5, arg2'=1, arg3'=arg3P_5, [ arg1P_5<=arg2 && arg3P_5<=arg2 && arg1>0 && arg2>-1 && arg1P_5>-1 && arg3P_5>-1 ], cost: 1 10: f236_0_main_InvokeMethod -> f358_0_duplicate_NULL : arg1'=arg1P_7, arg2'=0, arg3'=arg3P_7, [ arg1>0 && arg1P_7>0 && arg3P_7>0 && arg1P_7<=arg2 && arg3P_7<=arg2 && 1<=arg2 ], cost: 2 1: f1_0_main_Load -> f236_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>-1 ], cost: 1 2: f1_0_main_Load -> f208_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 9: f1_0_main_Load -> f208_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2>-1 && arg1>0 && arg1P_3>=1 ], cost: 1+arg1P_3 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 9: f1_0_main_Load -> f208_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2>-1 && arg1>0 && arg1P_3>=1 ], cost: 1+arg1P_3 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 11: __init -> f208_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_8>-1 && arg1P_8>0 && arg1P_3>=1 ], cost: 2+arg1P_3 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 11: __init -> f208_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_8>-1 && arg1P_8>0 && arg1P_3>=1 ], cost: 2+arg1P_3 Computing asymptotic complexity for rule 11 Resulting cost 0 has complexity: Unknown 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),?)