WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f291_0_solve_GE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && 0==arg2 && 0==arg1P_1 && 0==arg2P_1 ], cost: 1 1: f1_0_main_Load -> f291_0_solve_GE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>-1 && arg2>0 && arg1>0 && 1==arg2P_2 ], cost: 1 2: f291_0_solve_GE -> f291_0_solve_GE : arg1'=arg1P_3, arg2'=arg2P_3, [ -1+arg11 && -1+arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1 3: f291_0_solve_GE -> f291_0_solve_GE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2<2 && -1+arg11 && -1+arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_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, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f291_0_solve_GE : arg1'=0, arg2'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f291_0_solve_GE : arg1'=arg1P_2, arg2'=1, [ arg1P_2>-1 && arg2>0 && arg1>0 ], cost: 1 3: f291_0_solve_GE -> f291_0_solve_GE : arg1'=-1+arg1, [ arg2<2 && arg1>1 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 3: f291_0_solve_GE -> f291_0_solve_GE : arg1'=-1+arg1, [ arg2<2 && arg1>1 ], cost: 1 Accelerated rule 3 with backward acceleration, yielding the new rule 5. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 3. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f291_0_solve_GE : arg1'=0, arg2'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f291_0_solve_GE : arg1'=arg1P_2, arg2'=1, [ arg1P_2>-1 && arg2>0 && arg1>0 ], cost: 1 5: f291_0_solve_GE -> f291_0_solve_GE : arg1'=1, [ arg2<2 && -1+arg1>=0 ], cost: -1+arg1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f291_0_solve_GE : arg1'=0, arg2'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f291_0_solve_GE : arg1'=arg1P_2, arg2'=1, [ arg1P_2>-1 && arg2>0 && arg1>0 ], cost: 1 6: f1_0_main_Load -> f291_0_solve_GE : arg1'=1, arg2'=1, [ arg2>0 && arg1>0 && -1+arg1P_2>=0 ], cost: arg1P_2 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 6: f1_0_main_Load -> f291_0_solve_GE : arg1'=1, arg2'=1, [ arg2>0 && arg1>0 && -1+arg1P_2>=0 ], cost: arg1P_2 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 7: __init -> f291_0_solve_GE : arg1'=1, arg2'=1, [ arg2P_5>0 && arg1P_5>0 && -1+arg1P_2>=0 ], cost: 1+arg1P_2 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 7: __init -> f291_0_solve_GE : arg1'=1, arg2'=1, [ arg2P_5>0 && arg1P_5>0 && -1+arg1P_2>=0 ], cost: 1+arg1P_2 Computing asymptotic complexity for rule 7 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),?)