WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_New -> f536_0_copy_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>0 && arg1P_1>4 ], cost: 1 1: f536_0_copy_InvokeMethod -> f536_0_copy_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, [ 2+arg1P_2<=arg1 && 3+arg2P_2<=arg1 && arg1>2 && arg2>0 && arg1P_2>0 && arg2P_2>-1 ], cost: 1 2: f536_0_copy_InvokeMethod -> f536_0_copy_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, [ 2+arg1P_3<=arg1 && 3+arg2P_3<=arg1 && arg1>2 && arg2>0 && arg1P_3>0 && arg2P_3>-1 ], cost: 1 3: f536_0_copy_InvokeMethod -> f536_0_copy_InvokeMethod : arg1'=arg1P_4, arg2'=arg2P_4, [ 2+arg1P_4<=arg1 && 3+arg2P_4<=arg1 && arg1>2 && arg2>0 && arg1P_4>0 && arg2P_4>-1 ], cost: 1 4: __init -> f1_0_main_New : 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_New : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f536_0_copy_InvokeMethod -> f536_0_copy_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, [ 2+arg1P_2<=arg1 && 3+arg2P_2<=arg1 && arg1>2 && arg2>0 && arg1P_2>0 && arg2P_2>-1 ], cost: 1 2: f536_0_copy_InvokeMethod -> f536_0_copy_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, [ 2+arg1P_3<=arg1 && 3+arg2P_3<=arg1 && arg1>2 && arg2>0 && arg1P_3>0 && arg2P_3>-1 ], cost: 1 3: f536_0_copy_InvokeMethod -> f536_0_copy_InvokeMethod : arg1'=arg1P_4, arg2'=arg2P_4, [ 2+arg1P_4<=arg1 && 3+arg2P_4<=arg1 && arg1>2 && arg2>0 && arg1P_4>0 && arg2P_4>-1 ], cost: 1 Failed to prove monotonicity of the guard of rule 1. Failed to prove monotonicity of the guard of rule 2. Failed to prove monotonicity of the guard of rule 3. [accelerate] Nesting with 3 inner and 3 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_New -> f536_0_copy_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>0 && arg1P_1>4 ], cost: 1 1: f536_0_copy_InvokeMethod -> f536_0_copy_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, [ 2+arg1P_2<=arg1 && 3+arg2P_2<=arg1 && arg1>2 && arg2>0 && arg1P_2>0 && arg2P_2>-1 ], cost: 1 2: f536_0_copy_InvokeMethod -> f536_0_copy_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, [ 2+arg1P_3<=arg1 && 3+arg2P_3<=arg1 && arg1>2 && arg2>0 && arg1P_3>0 && arg2P_3>-1 ], cost: 1 3: f536_0_copy_InvokeMethod -> f536_0_copy_InvokeMethod : arg1'=arg1P_4, arg2'=arg2P_4, [ 2+arg1P_4<=arg1 && 3+arg2P_4<=arg1 && arg1>2 && arg2>0 && arg1P_4>0 && arg2P_4>-1 ], cost: 1 4: __init -> f1_0_main_New : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_New -> f536_0_copy_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>0 && arg1P_1>4 ], cost: 1 5: f1_0_main_New -> f536_0_copy_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>0 && arg2P_2>-1 ], cost: 2 6: f1_0_main_New -> f536_0_copy_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3>0 && arg2P_3>-1 ], cost: 2 7: f1_0_main_New -> f536_0_copy_InvokeMethod : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4>0 && arg2P_4>-1 ], cost: 2 4: __init -> f1_0_main_New : arg1'=arg1P_5, arg2'=arg2P_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),?)