WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f362_0_gt_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 && arg1P_1==arg3P_1 && arg2P_1==arg4P_1 && arg1P_1==arg5P_1 ], cost: 1 1: f362_0_gt_LE -> f362_0_gt_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg3>0 && arg4>0 && arg3==arg5 && arg1==arg1P_2 && arg2==arg2P_2 && -1+arg3==arg3P_2 && -1+arg4==arg4P_2 && -1+arg3==arg5P_2 ], cost: 1 2: f362_0_gt_LE -> f362_0_gt_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3>0 && 0==arg4 && arg3==arg5 && arg1==arg1P_3 && 1+arg2==arg2P_3 && arg1==arg3P_3 && 1+arg2==arg4P_3 && arg1==arg5P_3 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg3P_1, [ arg4P_1>-1 && arg2>-1 && arg3P_1>-1 && arg1>0 ], cost: 1 1: f362_0_gt_LE -> f362_0_gt_LE : arg3'=-1+arg3, arg4'=-1+arg4, arg5'=-1+arg3, [ arg3>0 && arg4>0 && arg3==arg5 ], cost: 1 2: f362_0_gt_LE -> f362_0_gt_LE : arg2'=1+arg2, arg3'=arg1, arg4'=1+arg2, arg5'=arg1, [ arg3>0 && 0==arg4 && arg3==arg5 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f362_0_gt_LE -> f362_0_gt_LE : arg3'=-1+arg3, arg4'=-1+arg4, arg5'=-1+arg3, [ arg3>0 && arg4>0 && arg3==arg5 ], cost: 1 2: f362_0_gt_LE -> f362_0_gt_LE : arg2'=1+arg2, arg3'=arg1, arg4'=1+arg2, arg5'=arg1, [ arg3>0 && 0==arg4 && arg3==arg5 ], cost: 1 Accelerated rule 1 with backward acceleration, yielding the new rule 4. Accelerated rule 1 with backward acceleration, yielding the new rule 5. [test] deduced invariant 1-arg1<=0 [test] deduced invariant -arg2+arg4<=0 [test] deduced invariant arg2-arg4<=0 Failed to prove monotonicity of the guard of rule 2. [accelerate] Nesting with 3 inner and 2 outer candidates Removing the simple loops: 1. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg3P_1, [ arg4P_1>-1 && arg2>-1 && arg3P_1>-1 && arg1>0 ], cost: 1 2: f362_0_gt_LE -> f362_0_gt_LE : arg2'=1+arg2, arg3'=arg1, arg4'=1+arg2, arg5'=arg1, [ arg3>0 && 0==arg4 && arg3==arg5 ], cost: 1 4: f362_0_gt_LE -> f362_0_gt_LE : arg3'=0, arg4'=-arg3+arg4, arg5'=0, [ arg3==arg5 && arg3>=1 && 1-arg3+arg4>0 ], cost: arg3 5: f362_0_gt_LE -> f362_0_gt_LE : arg3'=arg3-arg4, arg4'=0, arg5'=arg3-arg4, [ arg3==arg5 && arg4>=1 && 1+arg3-arg4>0 ], cost: arg4 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg3P_1, [ arg4P_1>-1 && arg2>-1 && arg3P_1>-1 && arg1>0 ], cost: 1 6: f1_0_main_Load -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=1, arg3'=arg3P_1, arg4'=1, arg5'=arg3P_1, [ arg2>-1 && arg1>0 && arg3P_1>0 ], cost: 2 7: f1_0_main_Load -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=0, arg4'=arg4P_1-arg3P_1, arg5'=0, [ arg4P_1>-1 && arg2>-1 && arg1>0 && arg3P_1>=1 && 1+arg4P_1-arg3P_1>0 ], cost: 1+arg3P_1 8: f1_0_main_Load -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=-arg4P_1+arg3P_1, arg4'=0, arg5'=-arg4P_1+arg3P_1, [ arg2>-1 && arg3P_1>-1 && arg1>0 && arg4P_1>=1 && 1-arg4P_1+arg3P_1>0 ], cost: 1+arg4P_1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 7: f1_0_main_Load -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=0, arg4'=arg4P_1-arg3P_1, arg5'=0, [ arg4P_1>-1 && arg2>-1 && arg1>0 && arg3P_1>=1 && 1+arg4P_1-arg3P_1>0 ], cost: 1+arg3P_1 8: f1_0_main_Load -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=-arg4P_1+arg3P_1, arg4'=0, arg5'=-arg4P_1+arg3P_1, [ arg2>-1 && arg3P_1>-1 && arg1>0 && arg4P_1>=1 && 1-arg4P_1+arg3P_1>0 ], cost: 1+arg4P_1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 9: __init -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=0, arg4'=arg4P_1-arg3P_1, arg5'=0, [ arg4P_1>-1 && arg2P_4>-1 && arg1P_4>0 && arg3P_1>=1 && 1+arg4P_1-arg3P_1>0 ], cost: 2+arg3P_1 10: __init -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=-arg4P_1+arg3P_1, arg4'=0, arg5'=-arg4P_1+arg3P_1, [ arg2P_4>-1 && arg3P_1>-1 && arg1P_4>0 && arg4P_1>=1 && 1-arg4P_1+arg3P_1>0 ], cost: 2+arg4P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 9: __init -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=0, arg4'=arg4P_1-arg3P_1, arg5'=0, [ arg4P_1>-1 && arg2P_4>-1 && arg1P_4>0 && arg3P_1>=1 && 1+arg4P_1-arg3P_1>0 ], cost: 2+arg3P_1 10: __init -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=-arg4P_1+arg3P_1, arg4'=0, arg5'=-arg4P_1+arg3P_1, [ arg2P_4>-1 && arg3P_1>-1 && arg1P_4>0 && arg4P_1>=1 && 1-arg4P_1+arg3P_1>0 ], cost: 2+arg4P_1 Computing asymptotic complexity for rule 9 Simplified the guard: 9: __init -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=0, arg4'=arg4P_1-arg3P_1, arg5'=0, [ arg2P_4>-1 && arg1P_4>0 && arg3P_1>=1 && 1+arg4P_1-arg3P_1>0 ], cost: 2+arg3P_1 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 10 Simplified the guard: 10: __init -> f362_0_gt_LE : arg1'=arg3P_1, arg2'=arg4P_1, arg3'=-arg4P_1+arg3P_1, arg4'=0, arg5'=-arg4P_1+arg3P_1, [ arg2P_4>-1 && arg1P_4>0 && arg4P_1>=1 && 1-arg4P_1+arg3P_1>0 ], cost: 2+arg4P_1 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),?)