WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f264_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 -> f264_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1>0 && arg1P_2>-1 && 1==arg2 && 0==arg2P_2 && arg1P_2==arg3P_2 ], cost: 1 2: f1_0_main_Load -> f264_0_loop_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2P_3>-1 && arg2>1 && arg1P_3>-1 && arg1>0 && arg1P_3==arg3P_3 ], cost: 1 3: f264_0_loop_LE -> f264_0_loop_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 && -1+arg2 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 -> f264_0_loop_LE : arg1'=0, arg2'=0, arg3'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f264_0_loop_LE : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [ arg1>0 && arg3P_2>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f264_0_loop_LE : arg1'=arg3P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2P_3>-1 && arg2>1 && arg3P_3>-1 && arg1>0 ], cost: 1 3: f264_0_loop_LE -> f264_0_loop_LE : arg1'=arg2+arg1, arg2'=-1+arg2, arg3'=arg2+arg1, [ arg1>0 && arg1==arg3 ], cost: 1 4: __init -> 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: f264_0_loop_LE -> f264_0_loop_LE : arg1'=arg2+arg1, arg2'=-1+arg2, arg3'=arg2+arg1, [ arg1>0 && arg1==arg3 ], 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 -> f264_0_loop_LE : arg1'=0, arg2'=0, arg3'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f264_0_loop_LE : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [ arg1>0 && arg3P_2>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f264_0_loop_LE : arg1'=arg3P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2P_3>-1 && arg2>1 && arg3P_3>-1 && arg1>0 ], cost: 1 3: f264_0_loop_LE -> f264_0_loop_LE : arg1'=arg2+arg1, arg2'=-1+arg2, arg3'=arg2+arg1, [ arg1>0 && arg1==arg3 ], cost: 1 4: __init -> 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 -> f264_0_loop_LE : arg1'=0, arg2'=0, arg3'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f264_0_loop_LE : arg1'=arg3P_2, arg2'=0, arg3'=arg3P_2, [ arg1>0 && arg3P_2>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f264_0_loop_LE : arg1'=arg3P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2P_3>-1 && arg2>1 && arg3P_3>-1 && arg1>0 ], cost: 1 5: f1_0_main_Load -> f264_0_loop_LE : arg1'=arg3P_2, arg2'=-1, arg3'=arg3P_2, [ arg1>0 && 1==arg2 && arg3P_2>0 ], cost: 2 6: f1_0_main_Load -> f264_0_loop_LE : arg1'=arg2P_3+arg3P_3, arg2'=-1+arg2P_3, arg3'=arg2P_3+arg3P_3, [ arg2P_3>-1 && arg2>1 && arg1>0 && arg3P_3>0 ], 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),?)