WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f210_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ x3_1>-1 && arg2>1 && x2_1>-1 && arg1>0 && -x2_1==arg1P_1 && -x3_1==arg2P_1 ], cost: 1 1: f210_0_main_LE -> f210_0_main_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2 f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f210_0_main_LE : arg1'=-x2_1, arg2'=-x3_1, [ x3_1>-1 && arg2>1 && x2_1>-1 && arg1>0 ], cost: 1 1: f210_0_main_LE -> f210_0_main_LE : arg1'=1+arg1, arg2'=arg2+arg1, [ arg2 f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f210_0_main_LE -> f210_0_main_LE : arg1'=1+arg1, arg2'=arg2+arg1, [ arg2 f210_0_main_LE : arg1'=-x2_1, arg2'=-x3_1, [ x3_1>-1 && arg2>1 && x2_1>-1 && arg1>0 ], cost: 1 1: f210_0_main_LE -> f210_0_main_LE : arg1'=1+arg1, arg2'=arg2+arg1, [ arg2 f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f210_0_main_LE : arg1'=-x2_1, arg2'=-x3_1, [ x3_1>-1 && arg2>1 && x2_1>-1 && arg1>0 ], cost: 1 3: f1_0_main_Load -> f210_0_main_LE : arg1'=1-x2_1, arg2'=-x3_1-x2_1, [ x3_1>-1 && arg2>1 && x2_1>-1 && arg1>0 && -x3_1<-x2_1 ], cost: 2 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 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),?)