WORST_CASE(INF,?) ### 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 During metering: Instantiating temporary variables by {arg1P_8==-1+arg1} Accelerated rule 7 with metering function arg1, yielding the new rule 9. Removing the simple loops: 7. 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 metering function -1+arg1, yielding the new rule 10. 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 9: f760_0_copy_NONNULL -> f760_0_copy_NONNULL : arg1'=0, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg2>0 && arg1>0 ], cost: arg1 10: f422_0_random_ArrayAccess -> f422_0_random_ArrayAccess : arg1'=1, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>1 && arg2P_7<=arg2 && arg2>0 && arg2P_7>0 ], 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 12: 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 && arg1P_6>1 && arg2P_7>0 && 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 11: f673_0_main_InvokeMethod -> f760_0_copy_NONNULL : arg1'=0, arg2'=arg3, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg1P_4<=arg2 && arg3>0 && arg1>0 && arg2>3 && arg1P_4>3 && 2+arg5<=arg2 && 4+arg4<=arg2 ], cost: 1+arg1P_4 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 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 12: 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 && arg1P_6>1 && arg2P_7>0 && 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 11: f673_0_main_InvokeMethod -> f760_0_copy_NONNULL : arg1'=0, arg2'=arg3, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg1P_4<=arg2 && arg3>0 && arg1>0 && arg2>3 && arg1P_4>3 && 2+arg5<=arg2 && 4+arg4<=arg2 ], cost: 1+arg1P_4 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 12: 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 && arg1P_6>1 && arg2P_7>0 && arg2P_7<=-3+arg1 ], cost: arg1P_6 14: f540_0_random_ArrayAccess -> f760_0_copy_NONNULL : arg1'=0, arg2'=arg3P_3, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ 3+arg1P_3<=arg1 && arg1>3 && arg1P_3>0 && arg2P_3>3 && 2+arg4<=arg1 && 0==arg3 && 1<=-1+arg2 && arg1P_4<=arg2P_3 && arg3P_3>0 && arg1P_4>3 && 2+arg4<=arg2P_3 && 4+arg4P_3<=arg2P_3 ], cost: 2+arg1P_4 13: __init -> f540_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_9, arg3'=0, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1P_9>0 && arg1P_2>3 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 15: __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 && arg1P_6>1 && arg2P_7>0 && arg2P_7<=-3+arg1P_2 ], cost: 2+arg1P_6 16: __init -> f760_0_copy_NONNULL : arg1'=0, arg2'=arg3P_3, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg1P_9>0 && arg1P_2>3 && 3+arg1P_3<=arg1P_2 && arg1P_3>0 && arg2P_3>3 && 2+arg4P_2<=arg1P_2 && 1<=-1+arg2P_9 && arg1P_4<=arg2P_3 && arg3P_3>0 && arg1P_4>3 && 2+arg4P_2<=arg2P_3 && 4+arg4P_3<=arg2P_3 ], cost: 4+arg1P_4 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 15: __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 && arg1P_6>1 && arg2P_7>0 && arg2P_7<=-3+arg1P_2 ], cost: 2+arg1P_6 16: __init -> f760_0_copy_NONNULL : arg1'=0, arg2'=arg3P_3, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg1P_9>0 && arg1P_2>3 && 3+arg1P_3<=arg1P_2 && arg1P_3>0 && arg2P_3>3 && 2+arg4P_2<=arg1P_2 && 1<=-1+arg2P_9 && arg1P_4<=arg2P_3 && arg3P_3>0 && arg1P_4>3 && 2+arg4P_2<=arg2P_3 && 4+arg4P_3<=arg2P_3 ], cost: 4+arg1P_4 Computing asymptotic complexity for rule 15 Simplified the guard: 15: __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 && arg1P_6>1 && arg2P_7>0 && arg2P_7<=-3+arg1P_2 ], cost: 2+arg1P_6 Solved the limit problem by the following transformations: Created initial limit problem: -2+arg1P_2-arg2P_7 (+/+!), -1+arg2P_9 (+/+!), -1+arg1P_6 (+/+!), 2+arg1P_6 (+), arg1P_9 (+/+!), arg2P_7 (+/+!), -1+arg1P_2-arg4P_2 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_2==4,arg2P_9==n,arg4P_2==2,arg1P_9==n,arg1P_6==n,arg2P_7==1} resulting limit problem: [solved] Solution: arg1P_2 / 4 arg2P_9 / n arg4P_2 / 2 arg1P_9 / n arg1P_6 / n arg2P_7 / 1 Resulting cost 2+n has complexity: Unbounded Found new complexity Unbounded. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Unbounded Cpx degree: Unbounded Solved cost: 2+n Rule cost: 2+arg1P_6 Rule guard: [ arg1P_9>0 && 2+arg4P_2<=arg1P_2 && 1<=-1+arg2P_9 && arg1P_6>1 && arg2P_7>0 && arg2P_7<=-3+arg1P_2 ] WORST_CASE(INF,?)