WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f91_0_divBy_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>0 && arg1>0 && 0==arg1P_1 ], cost: 1 1: f91_0_divBy_LE -> f91_0_divBy_LE\' : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>0 && arg2>x7_1 && x7_1>-1 && arg1>-1 && arg1==arg1P_2 && arg2==arg2P_2 ], cost: 1 2: f91_0_divBy_LE\' -> f91_0_divBy_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2>0 && arg2>arg2P_3 && arg1>-1 && arg2P_3>-1 && arg2-2*arg2P_3<2 && arg2-2*arg2P_3>=0 && arg2P_3+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 -> f91_0_divBy_LE : arg1'=0, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f91_0_divBy_LE -> f91_0_divBy_LE\' : [ arg1>-1 && 0<=-1+arg2 ], cost: 1 2: f91_0_divBy_LE\' -> f91_0_divBy_LE : arg1'=arg1P_3, arg2'=-arg1+arg1P_3, [ arg2>-arg1+arg1P_3 && arg1>-1 && -arg1+arg1P_3>-1 && arg2+2*arg1-2*arg1P_3<2 && arg2+2*arg1-2*arg1P_3>=0 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: __init 5: f91_0_divBy_LE -> f91_0_divBy_LE : arg1'=arg1P_3, arg2'=-arg1+arg1P_3, [ arg1>-1 && 0<=-1+arg2 && arg2>-arg1+arg1P_3 && -arg1+arg1P_3>-1 && arg2+2*arg1-2*arg1P_3<2 && arg2+2*arg1-2*arg1P_3>=0 ], cost: 2 4: __init -> f91_0_divBy_LE : arg1'=0, arg2'=arg2P_1, [ arg2P_1>-1 && arg2P_4>0 && arg1P_4>0 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 5: f91_0_divBy_LE -> f91_0_divBy_LE : arg1'=arg1P_3, arg2'=-arg1+arg1P_3, [ arg1>-1 && 0<=-1+arg2 && arg2>-arg1+arg1P_3 && -arg1+arg1P_3>-1 && arg2+2*arg1-2*arg1P_3<2 && arg2+2*arg1-2*arg1P_3>=0 ], cost: 2 Failed to prove monotonicity of the guard of rule 5. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 5: f91_0_divBy_LE -> f91_0_divBy_LE : arg1'=arg1P_3, arg2'=-arg1+arg1P_3, [ arg1>-1 && 0<=-1+arg2 && arg2>-arg1+arg1P_3 && -arg1+arg1P_3>-1 && arg2+2*arg1-2*arg1P_3<2 && arg2+2*arg1-2*arg1P_3>=0 ], cost: 2 4: __init -> f91_0_divBy_LE : arg1'=0, arg2'=arg2P_1, [ arg2P_1>-1 && arg2P_4>0 && arg1P_4>0 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 4: __init -> f91_0_divBy_LE : arg1'=0, arg2'=arg2P_1, [ arg2P_1>-1 && arg2P_4>0 && arg1P_4>0 ], cost: 2 6: __init -> f91_0_divBy_LE : arg1'=arg1P_3, arg2'=arg1P_3, [ arg1P_3>-1 && 1<=1+2*arg1P_3 ], 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),?)