WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f278_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 && arg2P_1==arg3P_1 && arg2P_1==arg4P_1 ], cost: 1 1: f278_0_main_LE -> f278_0_main_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg3>0 && 0==arg2 && arg3==arg4 && arg1==arg1P_2 && arg3==arg2P_2 && arg3==arg3P_2 && arg3==arg4P_2 ], cost: 1 2: f278_0_main_LE -> f278_0_main_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>0 && arg3>0 && arg2>0 && arg3==arg4 && -1+arg1==arg1P_3 && -1+arg2==arg2P_3 && arg3==arg3P_3 && arg3==arg4P_3 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_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, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f278_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f278_0_main_LE -> f278_0_main_LE : arg2'=arg3, arg4'=arg3, [ arg3>0 && 0==arg2 && arg3==arg4 ], cost: 1 2: f278_0_main_LE -> f278_0_main_LE : arg1'=-1+arg1, arg2'=-1+arg2, arg4'=arg3, [ arg1>0 && arg3>0 && arg2>0 && arg3==arg4 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f278_0_main_LE -> f278_0_main_LE : arg2'=arg3, arg4'=arg3, [ arg3>0 && 0==arg2 && arg3==arg4 ], cost: 1 2: f278_0_main_LE -> f278_0_main_LE : arg1'=-1+arg1, arg2'=-1+arg2, arg4'=arg3, [ arg1>0 && arg3>0 && arg2>0 && arg3==arg4 ], cost: 1 Failed to prove monotonicity of the guard of rule 1. Accelerated rule 2 with backward acceleration, yielding the new rule 4. Accelerated rule 2 with backward acceleration, yielding the new rule 5. [accelerate] Nesting with 3 inner and 2 outer candidates Removing the simple loops: 2. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f278_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f278_0_main_LE -> f278_0_main_LE : arg2'=arg3, arg4'=arg3, [ arg3>0 && 0==arg2 && arg3==arg4 ], cost: 1 4: f278_0_main_LE -> f278_0_main_LE : arg1'=0, arg2'=arg2-arg1, arg4'=arg3, [ arg3>0 && arg3==arg4 && arg1>=1 && 1+arg2-arg1>0 ], cost: arg1 5: f278_0_main_LE -> f278_0_main_LE : arg1'=-arg2+arg1, arg2'=0, arg4'=arg3, [ arg3>0 && arg3==arg4 && arg2>=1 && 1-arg2+arg1>0 ], cost: arg2 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f278_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1 6: f1_0_main_Load -> f278_0_main_LE : arg1'=0, arg2'=-arg1P_1+arg2P_1, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2>-1 && arg1>0 && arg2P_1>0 && arg1P_1>=1 && 1-arg1P_1+arg2P_1>0 ], cost: 1+arg1P_1 7: f1_0_main_Load -> f278_0_main_LE : arg1'=arg1P_1-arg2P_1, arg2'=0, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2>-1 && arg1P_1>-1 && arg1>0 && arg2P_1>0 && 1+arg1P_1-arg2P_1>0 ], cost: 1+arg2P_1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 6: f1_0_main_Load -> f278_0_main_LE : arg1'=0, arg2'=-arg1P_1+arg2P_1, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2>-1 && arg1>0 && arg2P_1>0 && arg1P_1>=1 && 1-arg1P_1+arg2P_1>0 ], cost: 1+arg1P_1 7: f1_0_main_Load -> f278_0_main_LE : arg1'=arg1P_1-arg2P_1, arg2'=0, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2>-1 && arg1P_1>-1 && arg1>0 && arg2P_1>0 && 1+arg1P_1-arg2P_1>0 ], cost: 1+arg2P_1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 8: __init -> f278_0_main_LE : arg1'=0, arg2'=-arg1P_1+arg2P_1, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2P_4>-1 && arg1P_4>0 && arg2P_1>0 && arg1P_1>=1 && 1-arg1P_1+arg2P_1>0 ], cost: 2+arg1P_1 9: __init -> f278_0_main_LE : arg1'=arg1P_1-arg2P_1, arg2'=0, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2P_4>-1 && arg1P_1>-1 && arg1P_4>0 && arg2P_1>0 && 1+arg1P_1-arg2P_1>0 ], cost: 2+arg2P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 8: __init -> f278_0_main_LE : arg1'=0, arg2'=-arg1P_1+arg2P_1, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2P_4>-1 && arg1P_4>0 && arg2P_1>0 && arg1P_1>=1 && 1-arg1P_1+arg2P_1>0 ], cost: 2+arg1P_1 9: __init -> f278_0_main_LE : arg1'=arg1P_1-arg2P_1, arg2'=0, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2P_4>-1 && arg1P_1>-1 && arg1P_4>0 && arg2P_1>0 && 1+arg1P_1-arg2P_1>0 ], cost: 2+arg2P_1 Computing asymptotic complexity for rule 8 Simplified the guard: 8: __init -> f278_0_main_LE : arg1'=0, arg2'=-arg1P_1+arg2P_1, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2P_4>-1 && arg1P_4>0 && arg1P_1>=1 && 1-arg1P_1+arg2P_1>0 ], cost: 2+arg1P_1 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 9 Simplified the guard: 9: __init -> f278_0_main_LE : arg1'=arg1P_1-arg2P_1, arg2'=0, arg3'=arg2P_1, arg4'=arg2P_1, [ arg2P_4>-1 && arg1P_4>0 && arg2P_1>0 && 1+arg1P_1-arg2P_1>0 ], cost: 2+arg2P_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),?)