WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1>0 && 0==arg2 && 0==arg1P_1 && 0==arg2P_1 && 0==arg3P_1 && 0==arg4P_1 && 0==arg5P_1 ], cost: 1 1: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1>0 && arg1P_2>-1 && 1==arg2 && 0==arg2P_2 && 0==arg3P_2 && 1==arg4P_2 && 1==arg5P_2 ], cost: 1 2: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3P_3>-1 && arg1P_3>-1 && arg1>0 && 2==arg2 && 0==arg2P_3 && 2==arg4P_3 && 2==arg5P_3 ], cost: 1 3: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1P_4>-1 && arg2>2 && x10_1>-1 && arg2P_4>-1 && arg1>0 && x10_1-arg2P_4==arg3P_4 && arg2==arg4P_4 && 3==arg5P_4 ], cost: 1 4: f293_0_loop_LT -> f293_0_loop_LT : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ 1+arg1>arg1 && arg1>-1 && arg3>0 && arg5>=arg4 && arg4>-1 && arg1==arg2 && 1+arg1==arg1P_5 && 1+arg1==arg2P_5 && 9-arg1==arg3P_5 && arg4==arg4P_5 && arg5==arg5P_5 ], cost: 1 5: f293_0_loop_LT -> f293_0_loop_LT : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg3>0 && 1+x19_1+arg1>=1 && arg4>-1 && arg5>-1 && arg5-1 && x19_1>-1 && arg1==arg2 && 1+x19_1+arg1==arg1P_6 && 1+x19_1+arg1==arg2P_6 && 9-x19_1-arg1==arg3P_6 && arg4==arg4P_6 && 1+arg5==arg5P_6 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_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, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f293_0_loop_LT : arg1'=0, arg2'=0, arg3'=0, arg4'=0, arg5'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_2, arg2'=0, arg3'=0, arg4'=1, arg5'=1, [ arg1>0 && arg1P_2>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_3, arg2'=0, arg3'=arg3P_3, arg4'=2, arg5'=2, [ arg3P_3>-1 && arg1P_3>-1 && arg1>0 && 2==arg2 ], cost: 1 3: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_4, arg2'=x10_1-arg3P_4, arg3'=arg3P_4, arg4'=arg2, arg5'=3, [ arg1P_4>-1 && arg2>2 && x10_1>-1 && x10_1-arg3P_4>-1 && arg1>0 ], cost: 1 4: f293_0_loop_LT -> f293_0_loop_LT : arg1'=1+arg1, arg2'=1+arg1, arg3'=9-arg1, [ arg1>-1 && arg3>0 && arg5>=arg4 && arg4>-1 && arg1==arg2 ], cost: 1 5: f293_0_loop_LT -> f293_0_loop_LT : arg1'=1+x19_1+arg1, arg2'=1+x19_1+arg1, arg3'=9-x19_1-arg1, arg5'=1+arg5, [ arg3>0 && arg5>-1 && arg5-1 && x19_1>-1 && arg1==arg2 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 4: f293_0_loop_LT -> f293_0_loop_LT : arg1'=1+arg1, arg2'=1+arg1, arg3'=9-arg1, [ arg1>-1 && arg3>0 && arg5>=arg4 && arg4>-1 && arg1==arg2 ], cost: 1 5: f293_0_loop_LT -> f293_0_loop_LT : arg1'=1+x19_1+arg1, arg2'=1+x19_1+arg1, arg3'=9-x19_1-arg1, arg5'=1+arg5, [ arg3>0 && arg5>-1 && arg5-1 && x19_1>-1 && arg1==arg2 ], cost: 1 Failed to prove monotonicity of the guard of rule 4. Failed to prove monotonicity of the guard of rule 5. [accelerate] Nesting with 2 inner and 2 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f293_0_loop_LT : arg1'=0, arg2'=0, arg3'=0, arg4'=0, arg5'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_2, arg2'=0, arg3'=0, arg4'=1, arg5'=1, [ arg1>0 && arg1P_2>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_3, arg2'=0, arg3'=arg3P_3, arg4'=2, arg5'=2, [ arg3P_3>-1 && arg1P_3>-1 && arg1>0 && 2==arg2 ], cost: 1 3: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_4, arg2'=x10_1-arg3P_4, arg3'=arg3P_4, arg4'=arg2, arg5'=3, [ arg1P_4>-1 && arg2>2 && x10_1>-1 && x10_1-arg3P_4>-1 && arg1>0 ], cost: 1 4: f293_0_loop_LT -> f293_0_loop_LT : arg1'=1+arg1, arg2'=1+arg1, arg3'=9-arg1, [ arg1>-1 && arg3>0 && arg5>=arg4 && arg4>-1 && arg1==arg2 ], cost: 1 5: f293_0_loop_LT -> f293_0_loop_LT : arg1'=1+x19_1+arg1, arg2'=1+x19_1+arg1, arg3'=9-x19_1-arg1, arg5'=1+arg5, [ arg3>0 && arg5>-1 && arg5-1 && x19_1>-1 && arg1==arg2 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f293_0_loop_LT : arg1'=0, arg2'=0, arg3'=0, arg4'=0, arg5'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_2, arg2'=0, arg3'=0, arg4'=1, arg5'=1, [ arg1>0 && arg1P_2>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_3, arg2'=0, arg3'=arg3P_3, arg4'=2, arg5'=2, [ arg3P_3>-1 && arg1P_3>-1 && arg1>0 && 2==arg2 ], cost: 1 3: f1_0_main_Load -> f293_0_loop_LT : arg1'=arg1P_4, arg2'=x10_1-arg3P_4, arg3'=arg3P_4, arg4'=arg2, arg5'=3, [ arg1P_4>-1 && arg2>2 && x10_1>-1 && x10_1-arg3P_4>-1 && arg1>0 ], cost: 1 7: f1_0_main_Load -> f293_0_loop_LT : arg1'=1, arg2'=1, arg3'=9, arg4'=2, arg5'=2, [ arg1>0 && 2==arg2 ], cost: 2 8: f1_0_main_Load -> f293_0_loop_LT : arg1'=1+x10_1-arg3P_4, arg2'=1+x10_1-arg3P_4, arg3'=9-x10_1+arg3P_4, arg4'=arg2, arg5'=3, [ x10_1-arg3P_4>-1 && 3-arg2==0 && x10_1>-1 && arg1>0 && arg3P_4>0 ], cost: 2 9: f1_0_main_Load -> f293_0_loop_LT : arg1'=1+x10_1+x19_1-arg3P_4, arg2'=1+x10_1+x19_1-arg3P_4, arg3'=9-x10_1-x19_1+arg3P_4, arg4'=arg2, arg5'=4, [ x10_1-arg3P_4>-1 && x10_1>-1 && arg1>0 && arg3P_4>0 && 3-1 ], cost: 2 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [], 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),?)