WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f117_0_createList_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f232_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ x7_1>-1 && arg2>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>3 && 0==arg3P_2 ], cost: 1 2: f1_0_main_Load -> f232_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ x12_1>-1 && arg2>0 && arg1>=arg1P_3 && arg1>=-1+arg2P_3 && arg1>0 && arg1P_3>0 && arg2P_3>1 && 0==arg3P_3 ], cost: 1 3: f117_0_createList_GE -> f117_0_createList_GE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 && -1+arg1 f389_0_dupList_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_5<=arg2 && x15_1>0 && 2+arg2P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>1 && arg2P_5>-1 && 0==arg3 && 0==arg3P_5 ], cost: 1 5: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ 2+arg1P_6<=arg1 && arg3<0 && arg1P_6<=arg2 && 3+arg2P_6<=arg1 && 1+arg2P_6<=arg2 && arg1>2 && arg2>0 && arg1P_6>0 && arg2P_6>-1 && 4+arg3P_6<=arg1 && 2+arg3<=arg1 && 2+arg3P_6<=arg2 ], cost: 1 6: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ 2+arg1P_7<=arg1 && arg3>0 && arg1P_7<=arg2 && 3+arg2P_7<=arg1 && 1+arg2P_7<=arg2 && arg1>2 && arg2>0 && arg1P_7>0 && arg2P_7>-1 && 4+arg3P_7<=arg1 && 2+arg3<=arg1 && 2+arg3P_7<=arg2 ], cost: 1 7: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1P_8<=arg1 && -2+arg1P_8<=arg2 && 2+arg2P_8<=arg1 && arg2P_8<=arg2 && arg1>2 && arg2>0 && arg1P_8>2 && arg2P_8>0 && 0==arg3 && 1==arg3P_8 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_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, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f117_0_createList_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f232_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=0, [ arg2>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>3 ], cost: 1 2: f1_0_main_Load -> f232_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=0, [ arg2>0 && arg1>=arg1P_3 && arg1>=-1+arg2P_3 && arg1>0 && arg1P_3>0 && arg2P_3>1 ], cost: 1 3: f117_0_createList_GE -> f117_0_createList_GE : arg1'=-1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1 4: f232_0_main_InvokeMethod -> f389_0_dupList_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=0, [ arg1P_5<=arg2 && 2+arg2P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>1 && arg2P_5>-1 && 0==arg3 ], cost: 1 5: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ 2+arg1P_6<=arg1 && arg3<0 && arg1P_6<=arg2 && 3+arg2P_6<=arg1 && 1+arg2P_6<=arg2 && arg1>2 && arg2>0 && arg1P_6>0 && arg2P_6>-1 && 4+arg3P_6<=arg1 && 2+arg3P_6<=arg2 ], cost: 1 6: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ 2+arg1P_7<=arg1 && arg3>0 && arg1P_7<=arg2 && 3+arg2P_7<=arg1 && 1+arg2P_7<=arg2 && arg1>2 && arg2>0 && arg1P_7>0 && arg2P_7>-1 && 4+arg3P_7<=arg1 && 2+arg3<=arg1 && 2+arg3P_7<=arg2 ], cost: 1 7: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=1, [ arg1P_8<=arg1 && -2+arg1P_8<=arg2 && 2+arg2P_8<=arg1 && arg2P_8<=arg2 && arg1>2 && arg2>0 && arg1P_8>2 && arg2P_8>0 && 0==arg3 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 3: f117_0_createList_GE -> f117_0_createList_GE : arg1'=-1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1 Accelerated rule 3 with metering function 1+arg1, yielding the new rule 9. Removing the simple loops: 3. Accelerating simple loops of location 3. Accelerating the following rules: 5: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ 2+arg1P_6<=arg1 && arg3<0 && arg1P_6<=arg2 && 3+arg2P_6<=arg1 && 1+arg2P_6<=arg2 && arg1>2 && arg2>0 && arg1P_6>0 && arg2P_6>-1 && 4+arg3P_6<=arg1 && 2+arg3P_6<=arg2 ], cost: 1 6: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ 2+arg1P_7<=arg1 && arg3>0 && arg1P_7<=arg2 && 3+arg2P_7<=arg1 && 1+arg2P_7<=arg2 && arg1>2 && arg2>0 && arg1P_7>0 && arg2P_7>-1 && 4+arg3P_7<=arg1 && 2+arg3<=arg1 && 2+arg3P_7<=arg2 ], cost: 1 7: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=1, [ arg1P_8<=arg1 && -2+arg1P_8<=arg2 && 2+arg2P_8<=arg1 && arg2P_8<=arg2 && arg1>2 && arg2>0 && arg1P_8>2 && arg2P_8>0 && 0==arg3 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_6==-2+arg1,arg2P_6==-3+arg1,arg3P_6==-2+arg2} Accelerated rule 5 with metering function -2+arg1-arg2, yielding the new rule 10. During metering: Instantiating temporary variables by {arg1P_7==-2+arg1,arg2P_7==-3+arg1,arg3P_7==-2+arg2} Accelerated rule 6 with metering function -2+arg1-arg2, yielding the new rule 11. Accelerated rule 7 with metering function -arg3, yielding the new rule 12. Removing the simple loops: 5 6 7. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f117_0_createList_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f232_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=0, [ arg2>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>3 ], cost: 1 2: f1_0_main_Load -> f232_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=0, [ arg2>0 && arg1>=arg1P_3 && arg1>=-1+arg2P_3 && arg1>0 && arg1P_3>0 && arg2P_3>1 ], cost: 1 9: f117_0_createList_GE -> f117_0_createList_GE : arg1'=-1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 ], cost: 1+arg1 4: f232_0_main_InvokeMethod -> f389_0_dupList_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=0, [ arg1P_5<=arg2 && 2+arg2P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>1 && arg2P_5>-1 && 0==arg3 ], cost: 1 10: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=4-arg1+2*arg2, arg2'=3-arg1+2*arg2, arg3'=3-arg1+2*arg2, [ arg3<0 && -2+arg1<=arg2 && arg1>2 && arg2>0 && -2+arg1-arg2>=1 ], cost: -2+arg1-arg2 11: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=4-arg1+2*arg2, arg2'=3-arg1+2*arg2, arg3'=3-arg1+2*arg2, [ arg3>0 && -2+arg1<=arg2 && arg1>2 && arg2>0 && 2+arg3<=arg1 && -2+arg1-arg2>=1 ], cost: -2+arg1-arg2 12: f389_0_dupList_NONNULL -> f389_0_dupList_NONNULL : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=1, [ arg1P_8<=arg1 && -2+arg1P_8<=arg2 && 2+arg2P_8<=arg1 && arg2P_8<=arg2 && arg1>2 && arg2>0 && arg1P_8>2 && arg2P_8>0 && 0==arg3 && -arg3>=1 ], cost: -arg3 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f117_0_createList_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f232_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=0, [ arg2>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>3 ], cost: 1 2: f1_0_main_Load -> f232_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=0, [ arg2>0 && arg1>=arg1P_3 && arg1>=-1+arg2P_3 && arg1>0 && arg1P_3>0 && arg2P_3>1 ], cost: 1 13: f1_0_main_Load -> f117_0_createList_GE : arg1'=-1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_1>-1 && arg2>0 && arg1>0 ], cost: 2+arg1P_1 4: f232_0_main_InvokeMethod -> f389_0_dupList_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=0, [ arg1P_5<=arg2 && 2+arg2P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>1 && arg2P_5>-1 && 0==arg3 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 13: f1_0_main_Load -> f117_0_createList_GE : arg1'=-1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_1>-1 && arg2>0 && arg1>0 ], cost: 2+arg1P_1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 14: __init -> f117_0_createList_GE : arg1'=-1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_1>-1 && arg2P_9>0 && arg1P_9>0 ], cost: 3+arg1P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 14: __init -> f117_0_createList_GE : arg1'=-1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_1>-1 && arg2P_9>0 && arg1P_9>0 ], cost: 3+arg1P_1 Computing asymptotic complexity for rule 14 Solved the limit problem by the following transformations: Created initial limit problem: 1+arg1P_1 (+/+!), arg2P_9 (+/+!), 3+arg1P_1 (+), arg1P_9 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg2P_9==n,arg1P_1==n,arg1P_9==n} resulting limit problem: [solved] Solution: arg2P_9 / n arg1P_1 / n arg1P_9 / n Resulting cost 3+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: 3+n Rule cost: 3+arg1P_1 Rule guard: [ arg1P_1>-1 && arg2P_9>0 && arg1P_9>0 ] WORST_CASE(INF,?)