WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f309_0_createList_Load -> f510_0_createList_Load : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, arg7'=arg7P_1, arg8'=arg8P_1, arg9'=arg9P_1, arg10'=arg10P_1, arg11'=arg11P_1, arg12'=arg12P_1, arg13'=arg13P_1, arg14'=arg14P_1, arg15'=arg15P_1, arg16'=arg16P_1, arg17'=arg17P_1, arg18'=arg18P_1, arg19'=arg19P_1, arg20'=arg20P_1, [ arg2P_1<=arg2 && arg2>9 && arg2P_1>9 && 3+arg7<=arg2 && 5+arg6<=arg2 && arg1==arg1P_1 && 0==arg3P_1 && 0==arg4P_1 && arg3==arg5P_1 && 0==arg7P_1 && 0==arg8P_1 && 0==arg9P_1 && arg3==arg13P_1 && arg4==arg14P_1 && arg4==arg15P_1 && arg5==arg17P_1 && arg6==arg18P_1 && arg7==arg19P_1 ], cost: 1 2: f510_0_createList_Load -> f673_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, arg7'=arg7P_3, arg8'=arg8P_3, arg9'=arg9P_3, arg10'=arg10P_3, arg11'=arg11P_3, arg12'=arg12P_3, arg13'=arg13P_3, arg14'=arg14P_3, arg15'=arg15P_3, arg16'=arg16P_3, arg17'=arg17P_3, arg18'=arg18P_3, arg19'=arg19P_3, arg20'=arg20P_3, [ arg2>11 && arg1P_3>11 && 3+arg19<=arg2 && 5+arg18<=arg2 && arg1==arg2P_3 && arg4==arg3P_3 && arg5==arg4P_3 && arg11==arg5P_3 && arg10==arg6P_3 && arg3==arg7P_3 && arg6==arg8P_3 && arg7==arg9P_3 && arg8==arg10P_3 && arg9==arg11P_3 && arg12==arg12P_3 && arg13==arg13P_3 && arg14==arg14P_3 && arg15==arg15P_3 && arg17==arg16P_3 && arg18==arg19P_3 && arg19==arg20P_3 ], cost: 1 1: f1_0_main_Load -> f309_0_createList_Load : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, arg6'=arg6P_2, arg7'=arg7P_2, arg8'=arg8P_2, arg9'=arg9P_2, arg10'=arg10P_2, arg11'=arg11P_2, arg12'=arg12P_2, arg13'=arg13P_2, arg14'=arg14P_2, arg15'=arg15P_2, arg16'=arg16P_2, arg17'=arg17P_2, arg18'=arg18P_2, arg19'=arg19P_2, arg20'=arg20P_2, [ arg1P_2>-1 && arg2>0 && -7+arg2P_2<=arg1 && arg1>0 && arg2P_2>7 && 1==arg5P_2 && 0==arg6P_2 && 0==arg7P_2 ], cost: 1 3: f673_0_createList_LE -> f673_0_createList_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, arg6'=arg6P_4, arg7'=arg7P_4, arg8'=arg8P_4, arg9'=arg9P_4, arg10'=arg10P_4, arg11'=arg11P_4, arg12'=arg12P_4, arg13'=arg13P_4, arg14'=arg14P_4, arg15'=arg15P_4, arg16'=arg16P_4, arg17'=arg17P_4, arg18'=arg18P_4, arg19'=arg19P_4, arg20'=arg20P_4, [ arg2>0 && x41_1>-1 && arg16>0 && arg160 && arg3>0 && arg7>0 && arg6>0 && arg5>0 && arg15>0 && x76_1>-1 && arg9>0 && arg12>0 && arg10>0 && arg14>0 && arg13>0 && arg11>0 && arg8>0 && arg20>-1 && arg19>-1 && arg1>11 && arg1P_4>11 && 11+arg17<=arg1 && 9+arg18<=arg1 && 3+arg20<=arg1 && 5+arg19<=arg1 && -1+arg2==arg2P_4 && arg3==arg3P_4 && arg4==arg4P_4 && 1+arg16==arg16P_4 && 1+arg19==arg19P_4 && 1+arg20==arg20P_4 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, arg7'=arg7P_5, arg8'=arg8P_5, arg9'=arg9P_5, arg10'=arg10P_5, arg11'=arg11P_5, arg12'=arg12P_5, arg13'=arg13P_5, arg14'=arg14P_5, arg15'=arg15P_5, arg16'=arg16P_5, arg17'=arg17P_5, arg18'=arg18P_5, arg19'=arg19P_5, arg20'=arg20P_5, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, arg7'=arg7P_5, arg8'=arg8P_5, arg9'=arg9P_5, arg10'=arg10P_5, arg11'=arg11P_5, arg12'=arg12P_5, arg13'=arg13P_5, arg14'=arg14P_5, arg15'=arg15P_5, arg16'=arg16P_5, arg17'=arg17P_5, arg18'=arg18P_5, arg19'=arg19P_5, arg20'=arg20P_5, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f309_0_createList_Load -> f510_0_createList_Load : arg2'=arg2P_1, arg3'=0, arg4'=0, arg5'=arg3, arg6'=arg6P_1, arg7'=0, arg8'=0, arg9'=0, arg10'=arg10P_1, arg11'=arg11P_1, arg12'=arg12P_1, arg13'=arg3, arg14'=arg4, arg15'=arg4, arg16'=arg16P_1, arg17'=arg5, arg18'=arg6, arg19'=arg7, arg20'=arg20P_1, [ arg2P_1<=arg2 && arg2>9 && arg2P_1>9 && 3+arg7<=arg2 && 5+arg6<=arg2 ], cost: 1 2: f510_0_createList_Load -> f673_0_createList_LE : arg1'=arg1P_3, arg2'=arg1, arg3'=arg4, arg4'=arg5, arg5'=arg11, arg6'=arg10, arg7'=arg3, arg8'=arg6, arg9'=arg7, arg10'=arg8, arg11'=arg9, arg16'=arg17, arg17'=arg17P_3, arg18'=arg18P_3, arg19'=arg18, arg20'=arg19, [ arg2>11 && arg1P_3>11 && 3+arg19<=arg2 && 5+arg18<=arg2 ], cost: 1 1: f1_0_main_Load -> f309_0_createList_Load : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=1, arg6'=0, arg7'=0, arg8'=arg8P_2, arg9'=arg9P_2, arg10'=arg10P_2, arg11'=arg11P_2, arg12'=arg12P_2, arg13'=arg13P_2, arg14'=arg14P_2, arg15'=arg15P_2, arg16'=arg16P_2, arg17'=arg17P_2, arg18'=arg18P_2, arg19'=arg19P_2, arg20'=arg20P_2, [ arg1P_2>-1 && arg2>0 && -7+arg2P_2<=arg1 && arg1>0 && arg2P_2>7 ], cost: 1 3: f673_0_createList_LE -> f673_0_createList_LE : arg1'=arg1P_4, arg2'=-1+arg2, arg5'=arg5P_4, arg6'=arg6P_4, arg7'=arg7P_4, arg8'=arg8P_4, arg9'=arg9P_4, arg10'=arg10P_4, arg11'=arg11P_4, arg12'=arg12P_4, arg13'=arg13P_4, arg14'=arg14P_4, arg15'=arg15P_4, arg16'=1+arg16, arg17'=arg17P_4, arg18'=arg18P_4, arg19'=1+arg19, arg20'=1+arg20, [ arg2>0 && arg16>0 && arg4>0 && arg3>0 && arg7>0 && arg6>0 && arg5>0 && arg15>0 && arg9>0 && arg12>0 && arg10>0 && arg14>0 && arg13>0 && arg11>0 && arg8>0 && arg20>-1 && arg19>-1 && arg1>11 && arg1P_4>11 && 11+arg17<=arg1 && 9+arg18<=arg1 && 3+arg20<=arg1 && 5+arg19<=arg1 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, arg7'=arg7P_5, arg8'=arg8P_5, arg9'=arg9P_5, arg10'=arg10P_5, arg11'=arg11P_5, arg12'=arg12P_5, arg13'=arg13P_5, arg14'=arg14P_5, arg15'=arg15P_5, arg16'=arg16P_5, arg17'=arg17P_5, arg18'=arg18P_5, arg19'=arg19P_5, arg20'=arg20P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 3. Accelerating the following rules: 3: f673_0_createList_LE -> f673_0_createList_LE : arg1'=arg1P_4, arg2'=-1+arg2, arg5'=arg5P_4, arg6'=arg6P_4, arg7'=arg7P_4, arg8'=arg8P_4, arg9'=arg9P_4, arg10'=arg10P_4, arg11'=arg11P_4, arg12'=arg12P_4, arg13'=arg13P_4, arg14'=arg14P_4, arg15'=arg15P_4, arg16'=1+arg16, arg17'=arg17P_4, arg18'=arg18P_4, arg19'=1+arg19, arg20'=1+arg20, [ arg2>0 && arg16>0 && arg4>0 && arg3>0 && arg7>0 && arg6>0 && arg5>0 && arg15>0 && arg9>0 && arg12>0 && arg10>0 && arg14>0 && arg13>0 && arg11>0 && arg8>0 && arg20>-1 && arg19>-1 && arg1>11 && arg1P_4>11 && 11+arg17<=arg1 && 9+arg18<=arg1 && 3+arg20<=arg1 && 5+arg19<=arg1 ], cost: 1 Failed to prove monotonicity of the guard of rule 3. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f309_0_createList_Load -> f510_0_createList_Load : arg2'=arg2P_1, arg3'=0, arg4'=0, arg5'=arg3, arg6'=arg6P_1, arg7'=0, arg8'=0, arg9'=0, arg10'=arg10P_1, arg11'=arg11P_1, arg12'=arg12P_1, arg13'=arg3, arg14'=arg4, arg15'=arg4, arg16'=arg16P_1, arg17'=arg5, arg18'=arg6, arg19'=arg7, arg20'=arg20P_1, [ arg2P_1<=arg2 && arg2>9 && arg2P_1>9 && 3+arg7<=arg2 && 5+arg6<=arg2 ], cost: 1 2: f510_0_createList_Load -> f673_0_createList_LE : arg1'=arg1P_3, arg2'=arg1, arg3'=arg4, arg4'=arg5, arg5'=arg11, arg6'=arg10, arg7'=arg3, arg8'=arg6, arg9'=arg7, arg10'=arg8, arg11'=arg9, arg16'=arg17, arg17'=arg17P_3, arg18'=arg18P_3, arg19'=arg18, arg20'=arg19, [ arg2>11 && arg1P_3>11 && 3+arg19<=arg2 && 5+arg18<=arg2 ], cost: 1 1: f1_0_main_Load -> f309_0_createList_Load : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=1, arg6'=0, arg7'=0, arg8'=arg8P_2, arg9'=arg9P_2, arg10'=arg10P_2, arg11'=arg11P_2, arg12'=arg12P_2, arg13'=arg13P_2, arg14'=arg14P_2, arg15'=arg15P_2, arg16'=arg16P_2, arg17'=arg17P_2, arg18'=arg18P_2, arg19'=arg19P_2, arg20'=arg20P_2, [ arg1P_2>-1 && arg2>0 && -7+arg2P_2<=arg1 && arg1>0 && arg2P_2>7 ], cost: 1 3: f673_0_createList_LE -> f673_0_createList_LE : arg1'=arg1P_4, arg2'=-1+arg2, arg5'=arg5P_4, arg6'=arg6P_4, arg7'=arg7P_4, arg8'=arg8P_4, arg9'=arg9P_4, arg10'=arg10P_4, arg11'=arg11P_4, arg12'=arg12P_4, arg13'=arg13P_4, arg14'=arg14P_4, arg15'=arg15P_4, arg16'=1+arg16, arg17'=arg17P_4, arg18'=arg18P_4, arg19'=1+arg19, arg20'=1+arg20, [ arg2>0 && arg16>0 && arg4>0 && arg3>0 && arg7>0 && arg6>0 && arg5>0 && arg15>0 && arg9>0 && arg12>0 && arg10>0 && arg14>0 && arg13>0 && arg11>0 && arg8>0 && arg20>-1 && arg19>-1 && arg1>11 && arg1P_4>11 && 11+arg17<=arg1 && 9+arg18<=arg1 && 3+arg20<=arg1 && 5+arg19<=arg1 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, arg7'=arg7P_5, arg8'=arg8P_5, arg9'=arg9P_5, arg10'=arg10P_5, arg11'=arg11P_5, arg12'=arg12P_5, arg13'=arg13P_5, arg14'=arg14P_5, arg15'=arg15P_5, arg16'=arg16P_5, arg17'=arg17P_5, arg18'=arg18P_5, arg19'=arg19P_5, arg20'=arg20P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f309_0_createList_Load -> f510_0_createList_Load : arg2'=arg2P_1, arg3'=0, arg4'=0, arg5'=arg3, arg6'=arg6P_1, arg7'=0, arg8'=0, arg9'=0, arg10'=arg10P_1, arg11'=arg11P_1, arg12'=arg12P_1, arg13'=arg3, arg14'=arg4, arg15'=arg4, arg16'=arg16P_1, arg17'=arg5, arg18'=arg6, arg19'=arg7, arg20'=arg20P_1, [ arg2P_1<=arg2 && arg2>9 && arg2P_1>9 && 3+arg7<=arg2 && 5+arg6<=arg2 ], cost: 1 2: f510_0_createList_Load -> f673_0_createList_LE : arg1'=arg1P_3, arg2'=arg1, arg3'=arg4, arg4'=arg5, arg5'=arg11, arg6'=arg10, arg7'=arg3, arg8'=arg6, arg9'=arg7, arg10'=arg8, arg11'=arg9, arg16'=arg17, arg17'=arg17P_3, arg18'=arg18P_3, arg19'=arg18, arg20'=arg19, [ arg2>11 && arg1P_3>11 && 3+arg19<=arg2 && 5+arg18<=arg2 ], cost: 1 5: f510_0_createList_Load -> f673_0_createList_LE : arg1'=arg1P_4, arg2'=-1+arg1, arg3'=arg4, arg4'=arg5, arg5'=arg5P_4, arg6'=arg6P_4, arg7'=arg7P_4, arg8'=arg8P_4, arg9'=arg9P_4, arg10'=arg10P_4, arg11'=arg11P_4, arg12'=arg12P_4, arg13'=arg13P_4, arg14'=arg14P_4, arg15'=arg15P_4, arg16'=1+arg17, arg17'=arg17P_4, arg18'=arg18P_4, arg19'=1+arg18, arg20'=1+arg19, [ arg2>11 && 3+arg19<=arg2 && 5+arg18<=arg2 && arg1>0 && arg17>0 && arg5>0 && arg4>0 && arg3>0 && arg10>0 && arg11>0 && arg15>0 && arg7>0 && arg12>0 && arg8>0 && arg14>0 && arg13>0 && arg9>0 && arg6>0 && arg19>-1 && arg18>-1 && arg1P_4>11 ], cost: 2 1: f1_0_main_Load -> f309_0_createList_Load : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=1, arg6'=0, arg7'=0, arg8'=arg8P_2, arg9'=arg9P_2, arg10'=arg10P_2, arg11'=arg11P_2, arg12'=arg12P_2, arg13'=arg13P_2, arg14'=arg14P_2, arg15'=arg15P_2, arg16'=arg16P_2, arg17'=arg17P_2, arg18'=arg18P_2, arg19'=arg19P_2, arg20'=arg20P_2, [ arg1P_2>-1 && arg2>0 && -7+arg2P_2<=arg1 && arg1>0 && arg2P_2>7 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, arg7'=arg7P_5, arg8'=arg8P_5, arg9'=arg9P_5, arg10'=arg10P_5, arg11'=arg11P_5, arg12'=arg12P_5, arg13'=arg13P_5, arg14'=arg14P_5, arg15'=arg15P_5, arg16'=arg16P_5, arg17'=arg17P_5, arg18'=arg18P_5, arg19'=arg19P_5, arg20'=arg20P_5, [], 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),?)