WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f164_0_createList_Return -> f346_0_main_NULL : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1<=arg1 && arg1>0 && arg2P_1>0 && 2+arg2<=arg1 && 0==arg1P_1 ], cost: 1 2: f346_0_main_NULL -> f346_0_main_NULL : arg1'=arg1P_3, arg2'=arg2P_3, [ 7+arg2P_3<=arg2 && arg2>6 && arg2P_3>-1 && 0==arg1 && 1==arg1P_3 ], cost: 1 3: f346_0_main_NULL -> f346_0_main_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>=-2+arg2P_4 && arg2>0 && arg2P_4>2 && 1==arg1 && 2==arg1P_4 ], cost: 1 4: f346_0_main_NULL -> f346_0_main_NULL : arg1'=arg1P_5, arg2'=arg2P_5, [ -4+arg2P_5<=arg2 && arg2>0 && arg2P_5>4 && 2==arg1 && 0==arg1P_5 ], cost: 1 1: f1_0_main_Load -> f346_0_main_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ x6_1>-1 && arg2>0 && arg1>0 && arg2P_2>0 && 0==arg1P_2 ], cost: 1 5: f1_0_main_Load -> f188_0_createList_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1P_6>-1 && arg2>0 && arg1>0 ], cost: 1 6: f188_0_createList_LE -> f188_0_createList_LE : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1>0 && -1+arg1==arg1P_7 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_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, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 2: f346_0_main_NULL -> f346_0_main_NULL : arg1'=arg1P_3, arg2'=arg2P_3, [ 7+arg2P_3<=arg2 && arg2>6 && arg2P_3>-1 && 0==arg1 && 1==arg1P_3 ], cost: 1 3: f346_0_main_NULL -> f346_0_main_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>=-2+arg2P_4 && arg2>0 && arg2P_4>2 && 1==arg1 && 2==arg1P_4 ], cost: 1 4: f346_0_main_NULL -> f346_0_main_NULL : arg1'=arg1P_5, arg2'=arg2P_5, [ -4+arg2P_5<=arg2 && arg2>0 && arg2P_5>4 && 2==arg1 && 0==arg1P_5 ], cost: 1 1: f1_0_main_Load -> f346_0_main_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ x6_1>-1 && arg2>0 && arg1>0 && arg2P_2>0 && 0==arg1P_2 ], cost: 1 5: f1_0_main_Load -> f188_0_createList_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1P_6>-1 && arg2>0 && arg1>0 ], cost: 1 6: f188_0_createList_LE -> f188_0_createList_LE : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1>0 && -1+arg1==arg1P_7 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Simplified all rules, resulting in: Start location: __init 2: f346_0_main_NULL -> f346_0_main_NULL : arg1'=1, arg2'=arg2P_3, [ 7+arg2P_3<=arg2 && arg2>6 && arg2P_3>-1 && 0==arg1 ], cost: 1 3: f346_0_main_NULL -> f346_0_main_NULL : arg1'=2, arg2'=arg2P_4, [ arg2>=-2+arg2P_4 && arg2>0 && arg2P_4>2 && 1==arg1 ], cost: 1 4: f346_0_main_NULL -> f346_0_main_NULL : arg1'=0, arg2'=arg2P_5, [ -4+arg2P_5<=arg2 && arg2>0 && arg2P_5>4 && 2==arg1 ], cost: 1 1: f1_0_main_Load -> f346_0_main_NULL : arg1'=0, arg2'=arg2P_2, [ arg2>0 && arg1>0 && arg2P_2>0 ], cost: 1 5: f1_0_main_Load -> f188_0_createList_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1P_6>-1 && arg2>0 && arg1>0 ], cost: 1 6: f188_0_createList_LE -> f188_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P_7, [ arg1>0 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 2: f346_0_main_NULL -> f346_0_main_NULL : arg1'=1, arg2'=arg2P_3, [ 7+arg2P_3<=arg2 && arg2>6 && arg2P_3>-1 && 0==arg1 ], cost: 1 3: f346_0_main_NULL -> f346_0_main_NULL : arg1'=2, arg2'=arg2P_4, [ arg2>=-2+arg2P_4 && arg2>0 && arg2P_4>2 && 1==arg1 ], cost: 1 4: f346_0_main_NULL -> f346_0_main_NULL : arg1'=0, arg2'=arg2P_5, [ -4+arg2P_5<=arg2 && arg2>0 && arg2P_5>4 && 2==arg1 ], cost: 1 Failed to prove monotonicity of the guard of rule 2. Failed to prove monotonicity of the guard of rule 3. Failed to prove monotonicity of the guard of rule 4. [accelerate] Nesting with 3 inner and 3 outer candidates Accelerating simple loops of location 3. Accelerating the following rules: 6: f188_0_createList_LE -> f188_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P_7, [ arg1>0 ], cost: 1 Accelerated rule 6 with backward acceleration, yielding the new rule 8. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 6. Accelerated all simple loops using metering functions (where possible): Start location: __init 2: f346_0_main_NULL -> f346_0_main_NULL : arg1'=1, arg2'=arg2P_3, [ 7+arg2P_3<=arg2 && arg2>6 && arg2P_3>-1 && 0==arg1 ], cost: 1 3: f346_0_main_NULL -> f346_0_main_NULL : arg1'=2, arg2'=arg2P_4, [ arg2>=-2+arg2P_4 && arg2>0 && arg2P_4>2 && 1==arg1 ], cost: 1 4: f346_0_main_NULL -> f346_0_main_NULL : arg1'=0, arg2'=arg2P_5, [ -4+arg2P_5<=arg2 && arg2>0 && arg2P_5>4 && 2==arg1 ], cost: 1 1: f1_0_main_Load -> f346_0_main_NULL : arg1'=0, arg2'=arg2P_2, [ arg2>0 && arg1>0 && arg2P_2>0 ], cost: 1 5: f1_0_main_Load -> f188_0_createList_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1P_6>-1 && arg2>0 && arg1>0 ], cost: 1 8: f188_0_createList_LE -> f188_0_createList_LE : arg1'=0, arg2'=arg2P_7, [ arg1>=1 ], cost: arg1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 1: f1_0_main_Load -> f346_0_main_NULL : arg1'=0, arg2'=arg2P_2, [ arg2>0 && arg1>0 && arg2P_2>0 ], cost: 1 5: f1_0_main_Load -> f188_0_createList_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1P_6>-1 && arg2>0 && arg1>0 ], cost: 1 9: f1_0_main_Load -> f346_0_main_NULL : arg1'=1, arg2'=arg2P_3, [ arg2>0 && arg1>0 && arg2P_3>-1 ], cost: 2 10: f1_0_main_Load -> f188_0_createList_LE : arg1'=0, arg2'=arg2P_7, [ arg2>0 && arg1>0 && arg1P_6>=1 ], cost: 1+arg1P_6 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 10: f1_0_main_Load -> f188_0_createList_LE : arg1'=0, arg2'=arg2P_7, [ arg2>0 && arg1>0 && arg1P_6>=1 ], cost: 1+arg1P_6 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 11: __init -> f188_0_createList_LE : arg1'=0, arg2'=arg2P_7, [ arg2P_8>0 && arg1P_8>0 && arg1P_6>=1 ], cost: 2+arg1P_6 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 11: __init -> f188_0_createList_LE : arg1'=0, arg2'=arg2P_7, [ arg2P_8>0 && arg1P_8>0 && arg1P_6>=1 ], cost: 2+arg1P_6 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),?)