WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>-1 && arg1P_1>1 && x3_1<2 && x3_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>-1 && arg1P_2>1 && x7_1>2 && arg1>0 ], cost: 1 2: f274_0_power_LE -> f274_0_power_LE\' : arg1'=arg1P_3, arg2'=arg2P_3, [ -2*x11_1+arg1==0 && arg1>x12_1 && arg1>0 && arg1==arg1P_3 ], cost: 1 4: f274_0_power_LE -> f274_0_power_LE\' : arg1'=arg1P_5, arg2'=arg2P_5, [ -2*x17_1+arg1==1 && arg1>x18_1 && arg1>0 && arg1==arg1P_5 ], cost: 1 3: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ -2*x15_1+arg1==0 && arg1>0 && arg1>arg1P_4 && -2*x15_1+arg1>=0 && -2*x15_1+arg1<2 && -2*arg1P_4+arg1<2 && -2*arg1P_4+arg1>=0 ], cost: 1 5: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ -2*x21_1+arg1==1 && arg1>0 && arg1>arg1P_6 && -2*x21_1+arg1>=0 && -2*x21_1+arg1<2 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>-1 && arg1P_1>1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f274_0_power_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>-1 && arg1P_2>1 && arg1>0 ], cost: 1 2: f274_0_power_LE -> f274_0_power_LE\' : arg2'=arg2P_3, [ -2*x11_1+arg1==0 && arg1>0 ], cost: 1 4: f274_0_power_LE -> f274_0_power_LE\' : arg2'=arg2P_5, [ -2*x17_1+arg1==1 && arg1>0 ], cost: 1 3: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ -2*x15_1+arg1==0 && arg1>arg1P_4 && -2*arg1P_4+arg1<2 && -2*arg1P_4+arg1>=0 ], cost: 1 5: f274_0_power_LE\' -> f274_0_power_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ -2*x21_1+arg1==1 && arg1>arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on tree-shaped paths): Start location: __init 9: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ -2*x11_1+arg1==0 && arg1>0 && -2*x15_1+arg1==0 && arg1>arg1P_4 && -2*arg1P_4+arg1<2 && -2*arg1P_4+arg1>=0 ], cost: 2 10: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ -2*x17_1+arg1==1 && arg1>0 && -2*x21_1+arg1==1 && arg1>arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 ], cost: 2 7: __init -> f274_0_power_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_7>-1 && arg1P_1>1 && arg1P_7>0 ], cost: 2 8: __init -> f274_0_power_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2P_7>-1 && arg1P_2>1 && arg1P_7>0 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 9: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ -2*x11_1+arg1==0 && arg1>0 && -2*x15_1+arg1==0 && arg1>arg1P_4 && -2*arg1P_4+arg1<2 && -2*arg1P_4+arg1>=0 ], cost: 2 10: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ -2*x17_1+arg1==1 && arg1>0 && -2*x21_1+arg1==1 && arg1>arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 ], cost: 2 Failed to prove monotonicity of the guard of rule 9. Failed to prove monotonicity of the guard of rule 10. [accelerate] Nesting with 2 inner and 2 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 9: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ -2*x11_1+arg1==0 && arg1>0 && -2*x15_1+arg1==0 && arg1>arg1P_4 && -2*arg1P_4+arg1<2 && -2*arg1P_4+arg1>=0 ], cost: 2 10: f274_0_power_LE -> f274_0_power_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ -2*x17_1+arg1==1 && arg1>0 && -2*x21_1+arg1==1 && arg1>arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 ], cost: 2 7: __init -> f274_0_power_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_7>-1 && arg1P_1>1 && arg1P_7>0 ], cost: 2 8: __init -> f274_0_power_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2P_7>-1 && arg1P_2>1 && arg1P_7>0 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 7: __init -> f274_0_power_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_7>-1 && arg1P_1>1 && arg1P_7>0 ], cost: 2 8: __init -> f274_0_power_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2P_7>-1 && arg1P_2>1 && arg1P_7>0 ], cost: 2 11: __init -> f274_0_power_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ 2*x15_1>1 && 2*x15_1>arg1P_4 && -2*arg1P_4+2*x15_1<2 && -2*arg1P_4+2*x15_1>=0 ], cost: 4 12: __init -> f274_0_power_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ 2*x15_1>1 && 2*x15_1>arg1P_4 && -2*arg1P_4+2*x15_1<2 && -2*arg1P_4+2*x15_1>=0 ], cost: 4 13: __init -> f274_0_power_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ 1+2*x21_1>1 && 1+2*x21_1>arg1P_6 && 1-2*arg1P_6+2*x21_1<2 && 1-2*arg1P_6+2*x21_1>=0 ], cost: 4 14: __init -> f274_0_power_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ 1+2*x21_1>1 && 1+2*x21_1>arg1P_6 && 1-2*arg1P_6+2*x21_1<2 && 1-2*arg1P_6+2*x21_1>=0 ], cost: 4 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),?)