WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>0 && x3_1>-1 && 1+arg1P_1<=arg1 && arg1>0 && arg1P_1>-1 && -1+x3_1==arg2P_1 ], cost: 1 1: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>-1 ], cost: 1 2: f152_0_createList_LE -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ -2+arg1P_3<=arg1 && arg2>0 && arg1>-1 && arg1P_3>0 && -1+arg2==arg2P_3 ], cost: 1 3: f196_0_reverse_NULL -> f196_0_reverse_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 1+arg1P_4<=arg1 && arg1>0 && arg1P_4>-1 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=-1+x3_1, [ arg2>0 && x3_1>-1 && 1+arg1P_1<=arg1 && arg1>0 && arg1P_1>-1 ], cost: 1 1: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>-1 ], cost: 1 2: f152_0_createList_LE -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=-1+arg2, [ -2+arg1P_3<=arg1 && arg2>0 && arg1>-1 && arg1P_3>0 ], cost: 1 3: f196_0_reverse_NULL -> f196_0_reverse_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 1+arg1P_4<=arg1 && arg1>0 && arg1P_4>-1 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 2: f152_0_createList_LE -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=-1+arg2, [ -2+arg1P_3<=arg1 && arg2>0 && arg1>-1 && arg1P_3>0 ], cost: 1 Accelerated rule 2 with backward acceleration, yielding the new rule 5. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 2. Accelerating simple loops of location 2. Accelerating the following rules: 3: f196_0_reverse_NULL -> f196_0_reverse_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 1+arg1P_4<=arg1 && arg1>0 && arg1P_4>-1 ], cost: 1 Failed to prove monotonicity of the guard of rule 3. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=-1+x3_1, [ arg2>0 && x3_1>-1 && 1+arg1P_1<=arg1 && arg1>0 && arg1P_1>-1 ], cost: 1 1: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>-1 ], cost: 1 5: f152_0_createList_LE -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=0, [ -2+arg1P_3<=arg1 && arg1>-1 && arg1P_3>0 && arg2>=1 ], cost: arg2 3: f196_0_reverse_NULL -> f196_0_reverse_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 1+arg1P_4<=arg1 && arg1>0 && arg1P_4>-1 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=-1+x3_1, [ arg2>0 && x3_1>-1 && 1+arg1P_1<=arg1 && arg1>0 && arg1P_1>-1 ], cost: 1 6: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=0, [ arg2>0 && arg1>0 && arg1P_3>0 && -1+x3_1>=1 && -2+arg1P_3<=-1+arg1 ], cost: x3_1 1: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>-1 ], cost: 1 7: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2<1 && arg1P_4>-1 && 1+arg1P_4<=arg1 && 1<=arg1 ], cost: 2 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 6: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=0, [ arg2>0 && arg1>0 && arg1P_3>0 && -1+x3_1>=1 && -2+arg1P_3<=-1+arg1 ], cost: x3_1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 8: __init -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=0, [ arg2P_5>0 && arg1P_5>0 && arg1P_3>0 && -1+x3_1>=1 && -2+arg1P_3<=-1+arg1P_5 ], cost: 1+x3_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 8: __init -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=0, [ arg2P_5>0 && arg1P_5>0 && arg1P_3>0 && -1+x3_1>=1 && -2+arg1P_3<=-1+arg1P_5 ], cost: 1+x3_1 Computing asymptotic complexity for rule 8 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),?)