WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f260_0_loop_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && 0==arg2 && 0==arg1P_1 && 0==arg2P_1 && 0==arg3P_1 ], cost: 1 1: f1_0_main_Load -> f260_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1>0 && x2_1>-1 && 1==arg2 && 0==arg1P_2 && -x2_1==arg2P_2 && 0==arg3P_2 ], cost: 1 2: f1_0_main_Load -> f260_0_loop_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ x5_1>-1 && arg2>1 && x6_1>-1 && arg1>0 && -x6_1==arg1P_3 && -x5_1==arg2P_3 && -x6_1==arg3P_3 ], cost: 1 3: f260_0_loop_LE -> f260_0_loop_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1arg2 && arg1<1+arg2 && arg1==arg3 && arg2+arg1==arg1P_4 && 1+arg2==arg2P_4 && arg2+arg1==arg3P_4 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_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, arg3'=arg3P_5, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f260_0_loop_LE : arg1'=0, arg2'=0, arg3'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f260_0_loop_LE : arg1'=0, arg2'=-x2_1, arg3'=0, [ arg1>0 && x2_1>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f260_0_loop_LE : arg1'=-x6_1, arg2'=-x5_1, arg3'=-x6_1, [ x5_1>-1 && arg2>1 && x6_1>-1 && arg1>0 ], cost: 1 3: f260_0_loop_LE -> f260_0_loop_LE : arg1'=arg2+arg1, arg2'=1+arg2, arg3'=arg2+arg1, [ arg1 f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 3: f260_0_loop_LE -> f260_0_loop_LE : arg1'=arg2+arg1, arg2'=1+arg2, arg3'=arg2+arg1, [ arg1 f260_0_loop_LE : arg1'=0, arg2'=0, arg3'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f260_0_loop_LE : arg1'=0, arg2'=-x2_1, arg3'=0, [ arg1>0 && x2_1>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f260_0_loop_LE : arg1'=-x6_1, arg2'=-x5_1, arg3'=-x6_1, [ x5_1>-1 && arg2>1 && x6_1>-1 && arg1>0 ], cost: 1 3: f260_0_loop_LE -> f260_0_loop_LE : arg1'=arg2+arg1, arg2'=1+arg2, arg3'=arg2+arg1, [ arg1 f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f260_0_loop_LE : arg1'=0, arg2'=0, arg3'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f260_0_loop_LE : arg1'=0, arg2'=-x2_1, arg3'=0, [ arg1>0 && x2_1>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f260_0_loop_LE : arg1'=-x6_1, arg2'=-x5_1, arg3'=-x6_1, [ x5_1>-1 && arg2>1 && x6_1>-1 && arg1>0 ], cost: 1 5: f1_0_main_Load -> f260_0_loop_LE : arg1'=-x6_1-x5_1, arg2'=1-x5_1, arg3'=-x6_1-x5_1, [ x5_1>-1 && arg2>1 && x6_1>-1 && arg1>0 && -x6_1<-x5_1 ], cost: 2 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [], 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),?)