WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 && 0==arg3P_1 ], cost: 1 1: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg4>-1 && arg3=-1+arg1P_2 && arg1>=arg2P_2 && arg2>=arg2P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && 2+arg4<=arg1 && 1+arg3==arg3P_2 && 1+arg4==arg4P_2 && arg5==arg5P_2 ], cost: 1 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_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, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 ], cost: 1 1: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3=-1+arg1P_2 && arg1>=arg2P_2 && arg2>=arg2P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && 2+arg4<=arg1 ], cost: 1 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3=-1+arg1P_2 && arg1>=arg2P_2 && arg2>=arg2P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && 2+arg4<=arg1 ], cost: 1 [test] deduced pseudo-invariant arg1P_2+arg2-arg2P_2-arg1<=0, also trying -arg1P_2-arg2+arg2P_2+arg1<=-1 Accelerated rule 1 with backward acceleration, yielding the new rule 3. Accelerated rule 1 with backward acceleration, yielding the new rule 4. [accelerate] Nesting with 2 inner and 1 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 ], cost: 1 1: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3=-1+arg1P_2 && arg1>=arg2P_2 && arg2>=arg2P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && 2+arg4<=arg1 ], cost: 1 3: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg5, arg4'=arg5-arg3+arg4, [ arg4>-1 && arg1>=-1+arg1P_2 && arg2>=arg2P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && arg1P_2+arg2-arg2P_2-arg1<=0 && arg5-arg3>=1 && arg1P_2>=arg2P_2 && 1+arg5-arg3+arg4<=arg1P_2 ], cost: arg5-arg3 4: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=-1+arg1P_2+arg3-arg4, arg4'=-1+arg1P_2, [ arg4>-1 && arg1>=-1+arg1P_2 && arg2>=arg2P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && arg1P_2+arg2-arg2P_2-arg1<=0 && -1+arg1P_2-arg4>=1 && -2+arg1P_2+arg3-arg4=arg2P_2 ], cost: -1+arg1P_2-arg4 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 ], cost: 1 5: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=1, arg4'=1+arg4P_1, arg5'=arg5P_1, [ arg2>1 && arg4P_1>-1 && arg1>0 && 00 && arg2P_2>0 && arg2P_2<=arg1 ], cost: 2 6: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2>1 && arg4P_1>-1 && arg1>0 && arg1P_2>0 && arg2P_2>0 && arg5P_1>=1 && arg1P_2>=arg2P_2 && 1+arg4P_1+arg5P_1<=arg1P_2 && arg2P_2<=arg1 ], cost: 1+arg5P_1 7: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=-1+arg1P_2-arg4P_1, arg4'=-1+arg1P_2, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg1>0 && arg1P_2>0 && arg2P_2>0 && -1+arg1P_2-arg4P_1>=1 && -2+arg1P_2-arg4P_1=arg2P_2 && arg2P_2<=arg1 ], cost: arg1P_2-arg4P_1 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 6: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2>1 && arg4P_1>-1 && arg1>0 && arg1P_2>0 && arg2P_2>0 && arg5P_1>=1 && arg1P_2>=arg2P_2 && 1+arg4P_1+arg5P_1<=arg1P_2 && arg2P_2<=arg1 ], cost: 1+arg5P_1 7: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=-1+arg1P_2-arg4P_1, arg4'=-1+arg1P_2, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg1>0 && arg1P_2>0 && arg2P_2>0 && -1+arg1P_2-arg4P_1>=1 && -2+arg1P_2-arg4P_1=arg2P_2 && arg2P_2<=arg1 ], cost: arg1P_2-arg4P_1 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 8: __init -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2P_3>1 && arg4P_1>-1 && arg1P_3>0 && arg1P_2>0 && arg2P_2>0 && arg5P_1>=1 && arg1P_2>=arg2P_2 && 1+arg4P_1+arg5P_1<=arg1P_2 && arg2P_2<=arg1P_3 ], cost: 2+arg5P_1 9: __init -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=-1+arg1P_2-arg4P_1, arg4'=-1+arg1P_2, arg5'=arg5P_1, [ arg5P_1>-1 && arg2P_3>1 && arg4P_1>-1 && arg1P_3>0 && arg1P_2>0 && arg2P_2>0 && -1+arg1P_2-arg4P_1>=1 && -2+arg1P_2-arg4P_1=arg2P_2 && arg2P_2<=arg1P_3 ], cost: 1+arg1P_2-arg4P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 8: __init -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2P_3>1 && arg4P_1>-1 && arg1P_3>0 && arg1P_2>0 && arg2P_2>0 && arg5P_1>=1 && arg1P_2>=arg2P_2 && 1+arg4P_1+arg5P_1<=arg1P_2 && arg2P_2<=arg1P_3 ], cost: 2+arg5P_1 9: __init -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=-1+arg1P_2-arg4P_1, arg4'=-1+arg1P_2, arg5'=arg5P_1, [ arg5P_1>-1 && arg2P_3>1 && arg4P_1>-1 && arg1P_3>0 && arg1P_2>0 && arg2P_2>0 && -1+arg1P_2-arg4P_1>=1 && -2+arg1P_2-arg4P_1=arg2P_2 && arg2P_2<=arg1P_3 ], cost: 1+arg1P_2-arg4P_1 Computing asymptotic complexity for rule 8 Simplified the guard: 8: __init -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2P_3>1 && arg4P_1>-1 && arg2P_2>0 && arg5P_1>=1 && arg1P_2>=arg2P_2 && 1+arg4P_1+arg5P_1<=arg1P_2 && arg2P_2<=arg1P_3 ], cost: 2+arg5P_1 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 9 Simplified the guard: 9: __init -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=-1+arg1P_2-arg4P_1, arg4'=-1+arg1P_2, arg5'=arg5P_1, [ arg2P_3>1 && arg4P_1>-1 && arg2P_2>0 && -1+arg1P_2-arg4P_1>=1 && -2+arg1P_2-arg4P_1=arg2P_2 && arg2P_2<=arg1P_3 ], cost: 1+arg1P_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),?)