WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f302_0_createList_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>-1 && arg2>0 && arg1>0 && arg2==arg2P_1 && 1==arg3P_1 ], cost: 1 1: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ x8_1>-1 && arg2>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 2: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ x14_1>-1 && arg2>0 && arg1>=arg1P_3 && arg1>=-1+arg2P_3 && arg1>0 && arg1P_3>0 && arg2P_3>1 ], cost: 1 3: f302_0_createList_GE -> f302_0_createList_GE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>-1 && arg2>-1 && arg3>0 && -1+arg1 f571_0_sumList_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ x18_1>0 && arg3>1 && arg1P_5<=arg2 && 1+arg2P_5<=arg2 && arg1>0 && arg2>0 && arg1P_5>0 && arg2P_5>-1 && arg3==arg3P_5 ], cost: 1 5: f571_0_sumList_NONNULL -> f571_0_sumList_NONNULL : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ 2+arg1P_6<=arg1 && arg3>1 && arg1P_6<=arg2 && 3+arg2P_6<=arg1 && 1+arg2P_6<=arg2 && arg1>2 && arg2>0 && arg1P_6>0 && arg2P_6>-1 && arg3==arg3P_6 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f302_0_createList_GE : arg1'=arg1P_1, arg3'=1, [ arg1P_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 2: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg1>=arg1P_3 && arg1>=-1+arg2P_3 && arg1>0 && arg1P_3>0 && arg2P_3>1 ], cost: 1 3: f302_0_createList_GE -> f302_0_createList_GE : arg1'=-1+arg1, arg3'=1+arg3, [ arg1>-1 && arg3>0 && arg3 f571_0_sumList_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, [ arg3>1 && arg1P_5<=arg2 && 1+arg2P_5<=arg2 && arg1>0 && arg2>0 && arg1P_5>0 && arg2P_5>-1 ], cost: 1 5: f571_0_sumList_NONNULL -> f571_0_sumList_NONNULL : arg1'=arg1P_6, arg2'=arg2P_6, [ 2+arg1P_6<=arg1 && arg3>1 && arg1P_6<=arg2 && 3+arg2P_6<=arg1 && 1+arg2P_6<=arg2 && arg1>2 && arg2>0 && arg1P_6>0 && arg2P_6>-1 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 3: f302_0_createList_GE -> f302_0_createList_GE : arg1'=-1+arg1, arg3'=1+arg3, [ arg1>-1 && arg3>0 && arg3 f571_0_sumList_NONNULL : arg1'=arg1P_6, arg2'=arg2P_6, [ 2+arg1P_6<=arg1 && arg3>1 && arg1P_6<=arg2 && 3+arg2P_6<=arg1 && 1+arg2P_6<=arg2 && arg1>2 && arg2>0 && arg1P_6>0 && arg2P_6>-1 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_6==-2+arg1,arg2P_6==-3+arg1} Accelerated rule 5 with metering function meter (where 2*meter==-2+arg1), yielding the new rule 7. Removing the simple loops: 5. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f302_0_createList_GE : arg1'=arg1P_1, arg3'=1, [ arg1P_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 2: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg1>=arg1P_3 && arg1>=-1+arg2P_3 && arg1>0 && arg1P_3>0 && arg2P_3>1 ], cost: 1 3: f302_0_createList_GE -> f302_0_createList_GE : arg1'=-1+arg1, arg3'=1+arg3, [ arg1>-1 && arg3>0 && arg3 f571_0_sumList_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, [ arg3>1 && arg1P_5<=arg2 && 1+arg2P_5<=arg2 && arg1>0 && arg2>0 && arg1P_5>0 && arg2P_5>-1 ], cost: 1 7: f571_0_sumList_NONNULL -> f571_0_sumList_NONNULL : arg1'=arg1-2*meter, arg2'=-1+arg1-2*meter, [ arg3>1 && -2+arg1<=arg2 && arg1>2 && arg2>0 && 2*meter==-2+arg1 && meter>=1 ], cost: meter 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f302_0_createList_GE : arg1'=arg1P_1, arg3'=1, [ arg1P_1>-1 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 2: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg1>=arg1P_3 && arg1>=-1+arg2P_3 && arg1>0 && arg1P_3>0 && arg2P_3>1 ], cost: 1 8: f1_0_main_Load -> f302_0_createList_GE : arg1'=-1+arg1P_1, arg3'=2, [ arg1P_1>-1 && arg1>0 && 1 f571_0_sumList_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, [ arg3>1 && arg1P_5<=arg2 && 1+arg2P_5<=arg2 && arg1>0 && arg2>0 && arg1P_5>0 && arg2P_5>-1 ], cost: 1 9: f502_0_main_InvokeMethod -> f571_0_sumList_NONNULL : arg1'=2, arg2'=1, [ arg3>1 && 2+2*meter<=arg2 && arg1>0 && 2+2*meter>2 && meter>=1 && 1<=-1+arg2 ], cost: 1+meter 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 1: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 2: f1_0_main_Load -> f502_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg1>=arg1P_3 && arg1>=-1+arg2P_3 && arg1>0 && arg1P_3>0 && arg2P_3>1 ], cost: 1 9: f502_0_main_InvokeMethod -> f571_0_sumList_NONNULL : arg1'=2, arg2'=1, [ arg3>1 && 2+2*meter<=arg2 && arg1>0 && 2+2*meter>2 && meter>=1 && 1<=-1+arg2 ], cost: 1+meter 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 9: f502_0_main_InvokeMethod -> f571_0_sumList_NONNULL : arg1'=2, arg2'=1, [ arg3>1 && 2+2*meter<=arg2 && arg1>0 && 2+2*meter>2 && meter>=1 && 1<=-1+arg2 ], cost: 1+meter 10: __init -> f502_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2P_7>0 && arg1P_2<=arg1P_7 && arg1P_7>0 && arg1P_2>0 && arg2P_2>2 ], cost: 2 11: __init -> f502_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2P_7>0 && arg1P_7>=arg1P_3 && arg1P_7>=-1+arg2P_3 && arg1P_7>0 && arg1P_3>0 && arg2P_3>1 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 12: __init -> f571_0_sumList_NONNULL : arg1'=2, arg2'=1, arg3'=arg3P_2, [ arg2P_7>0 && arg1P_2<=arg1P_7 && arg1P_7>0 && arg1P_2>0 && arg2P_2>2 && arg3P_2>1 && 2+2*meter<=arg2P_2 && 2+2*meter>2 && meter>=1 ], cost: 3+meter 13: __init -> f571_0_sumList_NONNULL : arg1'=2, arg2'=1, arg3'=arg3P_3, [ arg2P_7>0 && arg1P_7>=arg1P_3 && arg1P_7>=-1+arg2P_3 && arg1P_7>0 && arg1P_3>0 && arg2P_3>1 && arg3P_3>1 && 2+2*meter<=arg2P_3 && 2+2*meter>2 && meter>=1 ], cost: 3+meter ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 12: __init -> f571_0_sumList_NONNULL : arg1'=2, arg2'=1, arg3'=arg3P_2, [ arg2P_7>0 && arg1P_2<=arg1P_7 && arg1P_7>0 && arg1P_2>0 && arg2P_2>2 && arg3P_2>1 && 2+2*meter<=arg2P_2 && 2+2*meter>2 && meter>=1 ], cost: 3+meter 13: __init -> f571_0_sumList_NONNULL : arg1'=2, arg2'=1, arg3'=arg3P_3, [ arg2P_7>0 && arg1P_7>=arg1P_3 && arg1P_7>=-1+arg2P_3 && arg1P_7>0 && arg1P_3>0 && arg2P_3>1 && arg3P_3>1 && 2+2*meter<=arg2P_3 && 2+2*meter>2 && meter>=1 ], cost: 3+meter Computing asymptotic complexity for rule 12 Simplified the guard: 12: __init -> f571_0_sumList_NONNULL : arg1'=2, arg2'=1, arg3'=arg3P_2, [ arg2P_7>0 && arg1P_2<=arg1P_7 && arg1P_7>0 && arg1P_2>0 && arg3P_2>1 && 2+2*meter<=arg2P_2 && 2+2*meter>2 ], cost: 3+meter Solved the limit problem by the following transformations: Created initial limit problem: arg1P_7 (+/+!), 2*meter (+/+!), arg1P_2 (+/+!), 1+arg1P_7-arg1P_2 (+/+!), arg2P_7 (+/+!), 3+meter (+), -1+arg3P_2 (+/+!), -1+arg2P_2-2*meter (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_7==n,arg1P_2==n,arg2P_7==n,arg2P_2==2*n,arg3P_2==n,meter==-1+n} resulting limit problem: [solved] Solution: arg1P_7 / n arg1P_2 / n arg2P_7 / n arg2P_2 / 2*n arg3P_2 / n meter / -1+n 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: 3+meter Rule guard: [ arg2P_7>0 && arg1P_2<=arg1P_7 && arg1P_7>0 && arg1P_2>0 && arg3P_2>1 && 2+2*meter<=arg2P_2 && 2+2*meter>2 ] WORST_CASE(INF,?)