WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f182_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, [ x4_1>-1 && arg2>0 && arg1P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>2 ], cost: 1 1: f1_0_main_Load -> f182_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, [ x9_1>-1 && arg2>0 && arg1P_2<=arg1 && -1+arg2P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>1 ], cost: 1 3: f1_0_main_Load -> f117_0_createList_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4>-1 && arg2>0 && arg1>0 ], cost: 1 2: f182_0_main_InvokeMethod -> f274_0_growReduce_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3<=arg2 && x10_1>0 && arg1>0 && arg2>0 && arg2P_3>0 && 0==arg1P_3 ], cost: 1 5: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=arg1P_6, arg2'=arg2P_6, [ 1+arg2P_6<=arg2 && arg2>0 && arg2P_6>-1 && 0==arg1 && 1==arg1P_6 ], cost: 1 6: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=arg1P_7, arg2'=arg2P_7, [ 1+arg2P_7<=arg2 && arg2>0 && arg2P_7>-1 && 2==arg1 && 0==arg1P_7 ], cost: 1 7: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, [ -2+arg2P_8<=arg2 && arg2>0 && arg2P_8>2 && 1==arg1 && 2==arg1P_8 ], cost: 1 4: f117_0_createList_LE -> f117_0_createList_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>1 && -1+arg1 f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_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, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f182_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>0 && arg1P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>2 ], cost: 1 1: f1_0_main_Load -> f182_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>0 && arg1P_2<=arg1 && -1+arg2P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>1 ], cost: 1 3: f1_0_main_Load -> f117_0_createList_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4>-1 && arg2>0 && arg1>0 ], cost: 1 2: f182_0_main_InvokeMethod -> f274_0_growReduce_NONNULL : arg1'=0, arg2'=arg2P_3, [ arg2P_3<=arg2 && arg1>0 && arg2>0 && arg2P_3>0 ], cost: 1 5: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=1, arg2'=arg2P_6, [ 1+arg2P_6<=arg2 && arg2>0 && arg2P_6>-1 && 0==arg1 ], cost: 1 6: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=0, arg2'=arg2P_7, [ 1+arg2P_7<=arg2 && arg2>0 && arg2P_7>-1 && 2==arg1 ], cost: 1 7: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=2, arg2'=arg2P_8, [ -2+arg2P_8<=arg2 && arg2>0 && arg2P_8>2 && 1==arg1 ], cost: 1 4: f117_0_createList_LE -> f117_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P_5, [ arg1>1 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 5: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=1, arg2'=arg2P_6, [ 1+arg2P_6<=arg2 && arg2>0 && arg2P_6>-1 && 0==arg1 ], cost: 1 6: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=0, arg2'=arg2P_7, [ 1+arg2P_7<=arg2 && arg2>0 && arg2P_7>-1 && 2==arg1 ], cost: 1 7: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=2, arg2'=arg2P_8, [ -2+arg2P_8<=arg2 && arg2>0 && arg2P_8>2 && 1==arg1 ], cost: 1 Accelerated rule 5 with metering function -arg1, yielding the new rule 9. Accelerated rule 6 with metering function meter (where 2*meter==-2+arg1), yielding the new rule 10. Accelerated rule 7 with metering function 2-arg1, yielding the new rule 11. Removing the simple loops: 5 6 7. Accelerating simple loops of location 3. Accelerating the following rules: 4: f117_0_createList_LE -> f117_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P_5, [ arg1>1 ], cost: 1 Accelerated rule 4 with metering function -1+arg1, yielding the new rule 12. Removing the simple loops: 4. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f182_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>0 && arg1P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>2 ], cost: 1 1: f1_0_main_Load -> f182_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>0 && arg1P_2<=arg1 && -1+arg2P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>1 ], cost: 1 3: f1_0_main_Load -> f117_0_createList_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4>-1 && arg2>0 && arg1>0 ], cost: 1 2: f182_0_main_InvokeMethod -> f274_0_growReduce_NONNULL : arg1'=0, arg2'=arg2P_3, [ arg2P_3<=arg2 && arg1>0 && arg2>0 && arg2P_3>0 ], cost: 1 9: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=1, arg2'=arg2P_6, [ 1+arg2P_6<=arg2 && arg2>0 && arg2P_6>-1 && 0==arg1 && -arg1>=1 ], cost: -arg1 10: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=0, arg2'=arg2P_7, [ 1+arg2P_7<=arg2 && arg2>0 && arg2P_7>-1 && 2==arg1 && 2*meter==-2+arg1 && meter>=1 ], cost: meter 11: f274_0_growReduce_NONNULL -> f274_0_growReduce_NONNULL : arg1'=2, arg2'=arg2P_8, [ -2+arg2P_8<=arg2 && arg2>0 && arg2P_8>2 && 1==arg1 ], cost: 2-arg1 12: f117_0_createList_LE -> f117_0_createList_LE : arg1'=1, arg2'=arg2P_5, [ arg1>1 ], cost: -1+arg1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f182_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>0 && arg1P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>2 ], cost: 1 1: f1_0_main_Load -> f182_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>0 && arg1P_2<=arg1 && -1+arg2P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>1 ], cost: 1 3: f1_0_main_Load -> f117_0_createList_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4>-1 && arg2>0 && arg1>0 ], cost: 1 13: f1_0_main_Load -> f117_0_createList_LE : arg1'=1, arg2'=arg2P_5, [ arg2>0 && arg1>0 && arg1P_4>1 ], cost: arg1P_4 2: f182_0_main_InvokeMethod -> f274_0_growReduce_NONNULL : arg1'=0, arg2'=arg2P_3, [ arg2P_3<=arg2 && arg1>0 && arg2>0 && arg2P_3>0 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 13: f1_0_main_Load -> f117_0_createList_LE : arg1'=1, arg2'=arg2P_5, [ arg2>0 && arg1>0 && arg1P_4>1 ], cost: arg1P_4 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 14: __init -> f117_0_createList_LE : arg1'=1, arg2'=arg2P_5, [ arg2P_9>0 && arg1P_9>0 && arg1P_4>1 ], cost: 1+arg1P_4 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 14: __init -> f117_0_createList_LE : arg1'=1, arg2'=arg2P_5, [ arg2P_9>0 && arg1P_9>0 && arg1P_4>1 ], cost: 1+arg1P_4 Computing asymptotic complexity for rule 14 Solved the limit problem by the following transformations: Created initial limit problem: -1+arg1P_4 (+/+!), arg1P_9 (+/+!), 1+arg1P_4 (+), arg2P_9 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_4==n,arg1P_9==n,arg2P_9==n} resulting limit problem: [solved] Solution: arg1P_4 / n arg1P_9 / n arg2P_9 / n Resulting cost 1+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: 1+n Rule cost: 1+arg1P_4 Rule guard: [ arg2P_9>0 && arg1P_9>0 && arg1P_4>1 ] WORST_CASE(INF,?)