WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_New -> f169_0_exampleMethods_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>13 && 0==arg2P_1 && 10==arg3P_1 ], cost: 1 1: f169_0_exampleMethods_LE -> f169_0_exampleMethods_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>-1 && arg3>0 && arg1P_2<=arg1 && arg1>2 && arg1P_2>2 && 4+arg3<=arg1 && 10+arg2==arg2P_2 && -1+arg3==arg3P_2 ], cost: 1 2: __init -> f1_0_main_New : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 2: __init -> f1_0_main_New : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_New -> f169_0_exampleMethods_LE : arg1'=arg1P_1, arg2'=0, arg3'=10, [ arg1P_1>13 ], cost: 1 1: f169_0_exampleMethods_LE -> f169_0_exampleMethods_LE : arg1'=arg1P_2, arg2'=10+arg2, arg3'=-1+arg3, [ arg2>-1 && arg3>0 && arg1P_2<=arg1 && arg1>2 && arg1P_2>2 && 4+arg3<=arg1 ], cost: 1 2: __init -> f1_0_main_New : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f169_0_exampleMethods_LE -> f169_0_exampleMethods_LE : arg1'=arg1P_2, arg2'=10+arg2, arg3'=-1+arg3, [ arg2>-1 && arg3>0 && arg1P_2<=arg1 && arg1>2 && arg1P_2>2 && 4+arg3<=arg1 ], cost: 1 Failed to prove monotonicity of the guard of rule 1. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_New -> f169_0_exampleMethods_LE : arg1'=arg1P_1, arg2'=0, arg3'=10, [ arg1P_1>13 ], cost: 1 1: f169_0_exampleMethods_LE -> f169_0_exampleMethods_LE : arg1'=arg1P_2, arg2'=10+arg2, arg3'=-1+arg3, [ arg2>-1 && arg3>0 && arg1P_2<=arg1 && arg1>2 && arg1P_2>2 && 4+arg3<=arg1 ], cost: 1 2: __init -> f1_0_main_New : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_New -> f169_0_exampleMethods_LE : arg1'=arg1P_1, arg2'=0, arg3'=10, [ arg1P_1>13 ], cost: 1 3: f1_0_main_New -> f169_0_exampleMethods_LE : arg1'=arg1P_2, arg2'=10, arg3'=9, [ arg1P_2>2 ], cost: 2 2: __init -> f1_0_main_New : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [], 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),?)