WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f46_0_loop_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1 1: f46_0_loop_EQ -> f46_0_loop_EQ : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1<2 && arg1<0 && 1-arg1==arg1P_2 ], cost: 1 2: f46_0_loop_EQ -> f46_0_loop_EQ : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>0 && -1-arg1==arg1P_3 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f46_0_loop_EQ : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f46_0_loop_EQ -> f46_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P_2, [ arg1<0 ], cost: 1 2: f46_0_loop_EQ -> f46_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P_3, [ arg1>0 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f46_0_loop_EQ -> f46_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P_2, [ arg1<0 ], cost: 1 2: f46_0_loop_EQ -> f46_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P_3, [ arg1>0 ], cost: 1 Found no metering function for rule 1. Found no metering function for rule 2. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f46_0_loop_EQ : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 1: f46_0_loop_EQ -> f46_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P_2, [ arg1<0 ], cost: 1 2: f46_0_loop_EQ -> f46_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P_3, [ arg1>0 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f46_0_loop_EQ : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1 4: f1_0_main_Load -> f46_0_loop_EQ : arg1'=-1-arg2, arg2'=arg2P_3, [ arg1>0 && arg2>0 ], cost: 2 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], 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),?)