WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f289_0_appendNewList_Return -> f540_0_random_ArrayAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg2 && arg1>0 && arg2>3 && arg1P_1>3 && 2+arg5<=arg2 && 0==arg4 && 0==arg3P_1 && arg5==arg4P_1 ], cost: 1 2: f540_0_random_ArrayAccess -> f673_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ x51_1>0 && x51_1-1 && 3+arg1P_3<=arg1 && arg1>3 && arg1P_3>0 && arg2P_3>3 && 2+arg4<=arg1 && 0==arg3 && arg4==arg5P_3 ], cost: 1 5: f540_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ x59_1>0 && x59_1-1 && arg2>-1 && 3+arg2P_6<=arg1 && arg1>3 && arg2P_6>0 && 2+arg4<=arg1 && 0==arg3 ], cost: 1 1: f1_0_main_Load -> f540_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1>0 && arg1P_2>3 && arg2==arg2P_2 && 0==arg3P_2 ], cost: 1 4: f1_0_main_Load -> f422_0_random_ArrayAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2P_5<=arg1 && arg2>-1 && arg1>0 && arg2P_5>0 && 1==arg1P_5 ], cost: 1 3: f673_0_main_InvokeMethod -> f760_0_copy_NONNULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1P_4<=arg2 && arg3>0 && arg1>0 && arg2>3 && arg1P_4>3 && 2+arg5<=arg2 && 4+arg4<=arg2 && arg3==arg2P_4 ], cost: 1 7: f760_0_copy_NONNULL -> f760_0_copy_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ 1+arg1P_8<=arg1 && arg2>0 && arg1>0 && arg1P_8>-1 && arg2==arg2P_8 ], cost: 1 6: f422_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ x37_11 && x37_1>-1 && x41_1>-1 && x36_1>-1 && -1+arg10 && arg2P_7>0 && -1+arg1==arg1P_7 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 2: f540_0_random_ArrayAccess -> f673_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ x51_1>0 && x51_1-1 && 3+arg1P_3<=arg1 && arg1>3 && arg1P_3>0 && arg2P_3>3 && 2+arg4<=arg1 && 0==arg3 && arg4==arg5P_3 ], cost: 1 5: f540_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ x59_1>0 && x59_1-1 && arg2>-1 && 3+arg2P_6<=arg1 && arg1>3 && arg2P_6>0 && 2+arg4<=arg1 && 0==arg3 ], cost: 1 1: f1_0_main_Load -> f540_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1>0 && arg1P_2>3 && arg2==arg2P_2 && 0==arg3P_2 ], cost: 1 4: f1_0_main_Load -> f422_0_random_ArrayAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2P_5<=arg1 && arg2>-1 && arg1>0 && arg2P_5>0 && 1==arg1P_5 ], cost: 1 3: f673_0_main_InvokeMethod -> f760_0_copy_NONNULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1P_4<=arg2 && arg3>0 && arg1>0 && arg2>3 && arg1P_4>3 && 2+arg5<=arg2 && 4+arg4<=arg2 && arg3==arg2P_4 ], cost: 1 7: f760_0_copy_NONNULL -> f760_0_copy_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ 1+arg1P_8<=arg1 && arg2>0 && arg1>0 && arg1P_8>-1 && arg2==arg2P_8 ], cost: 1 6: f422_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ x37_11 && x37_1>-1 && x41_1>-1 && x36_1>-1 && -1+arg10 && arg2P_7>0 && -1+arg1==arg1P_7 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Simplified all rules, resulting in: Start location: __init 2: f540_0_random_ArrayAccess -> f673_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg4, [ 3+arg1P_3<=arg1 && arg1>3 && arg1P_3>0 && arg2P_3>3 && 2+arg4<=arg1 && 0==arg3 && 1<=-1+arg2 ], cost: 1 5: f540_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1P_6>-1 && 3+arg2P_6<=arg1 && arg1>3 && arg2P_6>0 && 2+arg4<=arg1 && 0==arg3 && 1<=-1+arg2 ], cost: 1 1: f1_0_main_Load -> f540_0_random_ArrayAccess : arg1'=arg1P_2, arg3'=0, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1>0 && arg1P_2>3 ], cost: 1 4: f1_0_main_Load -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2P_5<=arg1 && arg2>-1 && arg1>0 && arg2P_5>0 ], cost: 1 3: f673_0_main_InvokeMethod -> f760_0_copy_NONNULL : arg1'=arg1P_4, arg2'=arg3, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1P_4<=arg2 && arg3>0 && arg1>0 && arg2>3 && arg1P_4>3 && 2+arg5<=arg2 && 4+arg4<=arg2 ], cost: 1 7: f760_0_copy_NONNULL -> f760_0_copy_NONNULL : arg1'=arg1P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ 1+arg1P_8<=arg1 && arg2>0 && arg1>0 && arg1P_8>-1 ], cost: 1 6: f422_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=-1+arg1, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>1 && arg2P_7<=arg2 && arg2>0 && arg2P_7>0 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 4. Accelerating the following rules: 7: f760_0_copy_NONNULL -> f760_0_copy_NONNULL : arg1'=arg1P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ 1+arg1P_8<=arg1 && arg2>0 && arg1>0 && arg1P_8>-1 ], cost: 1 Failed to prove monotonicity of the guard of rule 7. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerating simple loops of location 5. Accelerating the following rules: 6: f422_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=-1+arg1, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>1 && arg2P_7<=arg2 && arg2>0 && arg2P_7>0 ], cost: 1 Accelerated rule 6 with backward acceleration, yielding the new rule 9. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 6. Accelerated all simple loops using metering functions (where possible): Start location: __init 2: f540_0_random_ArrayAccess -> f673_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg4, [ 3+arg1P_3<=arg1 && arg1>3 && arg1P_3>0 && arg2P_3>3 && 2+arg4<=arg1 && 0==arg3 && 1<=-1+arg2 ], cost: 1 5: f540_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1P_6>-1 && 3+arg2P_6<=arg1 && arg1>3 && arg2P_6>0 && 2+arg4<=arg1 && 0==arg3 && 1<=-1+arg2 ], cost: 1 1: f1_0_main_Load -> f540_0_random_ArrayAccess : arg1'=arg1P_2, arg3'=0, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1>0 && arg1P_2>3 ], cost: 1 4: f1_0_main_Load -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2P_5<=arg1 && arg2>-1 && arg1>0 && arg2P_5>0 ], cost: 1 3: f673_0_main_InvokeMethod -> f760_0_copy_NONNULL : arg1'=arg1P_4, arg2'=arg3, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1P_4<=arg2 && arg3>0 && arg1>0 && arg2>3 && arg1P_4>3 && 2+arg5<=arg2 && 4+arg4<=arg2 ], cost: 1 7: f760_0_copy_NONNULL -> f760_0_copy_NONNULL : arg1'=arg1P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ 1+arg1P_8<=arg1 && arg2>0 && arg1>0 && arg1P_8>-1 ], cost: 1 9: f422_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg2P_7<=arg2 && arg2>0 && arg2P_7>0 && -1+arg1>=1 ], cost: -1+arg1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 2: f540_0_random_ArrayAccess -> f673_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg4, [ 3+arg1P_3<=arg1 && arg1>3 && arg1P_3>0 && arg2P_3>3 && 2+arg4<=arg1 && 0==arg3 && 1<=-1+arg2 ], cost: 1 5: f540_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1P_6>-1 && 3+arg2P_6<=arg1 && arg1>3 && arg2P_6>0 && 2+arg4<=arg1 && 0==arg3 && 1<=-1+arg2 ], cost: 1 11: f540_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>3 && 2+arg4<=arg1 && 0==arg3 && 1<=-1+arg2 && arg2P_7>0 && -1+arg1P_6>=1 && arg2P_7<=-3+arg1 ], cost: arg1P_6 1: f1_0_main_Load -> f540_0_random_ArrayAccess : arg1'=arg1P_2, arg3'=0, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1>0 && arg1P_2>3 ], cost: 1 4: f1_0_main_Load -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2P_5<=arg1 && arg2>-1 && arg1>0 && arg2P_5>0 ], cost: 1 3: f673_0_main_InvokeMethod -> f760_0_copy_NONNULL : arg1'=arg1P_4, arg2'=arg3, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1P_4<=arg2 && arg3>0 && arg1>0 && arg2>3 && arg1P_4>3 && 2+arg5<=arg2 && 4+arg4<=arg2 ], cost: 1 10: f673_0_main_InvokeMethod -> f760_0_copy_NONNULL : arg1'=arg1P_8, arg2'=arg3, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg3>0 && arg1>0 && arg2>3 && 2+arg5<=arg2 && 4+arg4<=arg2 && arg1P_8>-1 && 1+arg1P_8<=arg2 ], cost: 2 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 11: f540_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>3 && 2+arg4<=arg1 && 0==arg3 && 1<=-1+arg2 && arg2P_7>0 && -1+arg1P_6>=1 && arg2P_7<=-3+arg1 ], cost: arg1P_6 1: f1_0_main_Load -> f540_0_random_ArrayAccess : arg1'=arg1P_2, arg3'=0, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1>0 && arg1P_2>3 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 13: __init -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1P_9>0 && arg1P_2>3 && 2+arg4P_2<=arg1P_2 && 1<=-1+arg2P_9 && arg2P_7>0 && -1+arg1P_6>=1 && arg2P_7<=-3+arg1P_2 ], cost: 2+arg1P_6 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 13: __init -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1P_9>0 && arg1P_2>3 && 2+arg4P_2<=arg1P_2 && 1<=-1+arg2P_9 && arg2P_7>0 && -1+arg1P_6>=1 && arg2P_7<=-3+arg1P_2 ], cost: 2+arg1P_6 Computing asymptotic complexity for rule 13 Simplified the guard: 13: __init -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1P_9>0 && 2+arg4P_2<=arg1P_2 && 1<=-1+arg2P_9 && arg2P_7>0 && -1+arg1P_6>=1 && arg2P_7<=-3+arg1P_2 ], cost: 2+arg1P_6 Resulting cost 0 has complexity: Unknown 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),?)