WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_New -> f73_0_m_GE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1>1 && 0==arg2P_1 ], cost: 1 1: f73_0_m_GE -> f73_0_m_GE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2<10 && arg2>-1 && -1+arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && 2+arg2<=arg1 && 1+arg2==arg2P_2 ], cost: 1 2: __init -> f1_0_main_New : arg1'=arg1P_3, arg2'=arg2P_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, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_New -> f73_0_m_GE : arg1'=arg1P_1, arg2'=0, [ arg1P_1>1 ], cost: 1 1: f73_0_m_GE -> f73_0_m_GE : arg1'=arg1P_2, arg2'=1+arg2, [ arg2<10 && arg2>-1 && -1+arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && 2+arg2<=arg1 ], cost: 1 2: __init -> f1_0_main_New : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f73_0_m_GE -> f73_0_m_GE : arg1'=arg1P_2, arg2'=1+arg2, [ arg2<10 && arg2>-1 && -1+arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && 2+arg2<=arg1 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_2==1+arg1} Accelerated rule 1 with metering function 10-arg2, yielding the new rule 3. Removing the simple loops: 1. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_New -> f73_0_m_GE : arg1'=arg1P_1, arg2'=0, [ arg1P_1>1 ], cost: 1 3: f73_0_m_GE -> f73_0_m_GE : arg1'=10+arg1-arg2, arg2'=10, [ arg2<10 && arg2>-1 && arg1>0 && 2+arg2<=arg1 ], cost: 10-arg2 2: __init -> f1_0_main_New : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_New -> f73_0_m_GE : arg1'=arg1P_1, arg2'=0, [ arg1P_1>1 ], cost: 1 4: f1_0_main_New -> f73_0_m_GE : arg1'=10+arg1P_1, arg2'=10, [ arg1P_1>1 ], cost: 11 2: __init -> f1_0_main_New : arg1'=arg1P_3, arg2'=arg2P_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),?)