WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>0 && x3_1>-1 && 1+arg1P_1<=arg1 && arg1>0 && arg1P_1>-1 && -1+x3_1==arg2P_1 ], cost: 1 1: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>-1 ], cost: 1 2: f152_0_createList_LE -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ -2+arg1P_3<=arg1 && arg2>0 && arg1>-1 && arg1P_3>0 && -1+arg2==arg2P_3 ], cost: 1 3: f196_0_reverse_NULL -> f196_0_reverse_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 1+arg1P_4<=arg1 && arg1>0 && arg1P_4>-1 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=-1+x3_1, [ arg2>0 && x3_1>-1 && 1+arg1P_1<=arg1 && arg1>0 && arg1P_1>-1 ], cost: 1 1: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>-1 ], cost: 1 2: f152_0_createList_LE -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=-1+arg2, [ -2+arg1P_3<=arg1 && arg2>0 && arg1>-1 && arg1P_3>0 ], cost: 1 3: f196_0_reverse_NULL -> f196_0_reverse_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 1+arg1P_4<=arg1 && arg1>0 && arg1P_4>-1 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 2: f152_0_createList_LE -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=-1+arg2, [ -2+arg1P_3<=arg1 && arg2>0 && arg1>-1 && arg1P_3>0 ], cost: 1 Accelerated rule 2 with metering function arg2, yielding the new rule 5. Removing the simple loops: 2. Accelerating simple loops of location 2. Accelerating the following rules: 3: f196_0_reverse_NULL -> f196_0_reverse_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 1+arg1P_4<=arg1 && arg1>0 && arg1P_4>-1 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_4==-1+arg1} Accelerated rule 3 with metering function arg1, yielding the new rule 6. Removing the simple loops: 3. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=-1+x3_1, [ arg2>0 && x3_1>-1 && 1+arg1P_1<=arg1 && arg1>0 && arg1P_1>-1 ], cost: 1 1: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>-1 ], cost: 1 5: f152_0_createList_LE -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=0, [ -2+arg1P_3<=arg1 && arg2>0 && arg1>-1 && arg1P_3>0 ], cost: arg2 6: f196_0_reverse_NULL -> f196_0_reverse_NULL : arg1'=0, arg2'=arg2P_4, [ arg1>0 ], cost: arg1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=-1+x3_1, [ arg2>0 && x3_1>-1 && 1+arg1P_1<=arg1 && arg1>0 && arg1P_1>-1 ], cost: 1 7: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=0, [ arg2>0 && arg1>0 && -1+x3_1>0 && arg1P_3>0 && -2+arg1P_3<=-1+arg1 ], cost: x3_1 1: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>-1 ], cost: 1 8: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=0, arg2'=arg2P_4, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>0 ], cost: 1+arg1P_2 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=-1+x3_1, [ arg2>0 && x3_1>-1 && 1+arg1P_1<=arg1 && arg1>0 && arg1P_1>-1 ], cost: 1 7: f1_0_main_Load -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=0, [ arg2>0 && arg1>0 && -1+x3_1>0 && arg1P_3>0 && -2+arg1P_3<=-1+arg1 ], cost: x3_1 8: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=0, arg2'=arg2P_4, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>0 ], cost: 1+arg1P_2 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 8: f152_0_createList_LE -> f196_0_reverse_NULL : arg1'=0, arg2'=arg2P_4, [ arg1P_2<=arg1 && arg2<1 && arg1>-1 && arg1P_2>0 ], cost: 1+arg1P_2 9: __init -> f152_0_createList_LE : arg1'=arg1P_1, arg2'=-1+x3_1, [ arg2P_5>0 && x3_1>-1 && 1+arg1P_1<=arg1P_5 && arg1P_5>0 && arg1P_1>-1 ], cost: 2 10: __init -> f152_0_createList_LE : arg1'=arg1P_3, arg2'=0, [ arg2P_5>0 && arg1P_5>0 && -1+x3_1>0 && arg1P_3>0 && -2+arg1P_3<=-1+arg1P_5 ], cost: 1+x3_1 Eliminated locations (on tree-shaped paths): Start location: __init 11: __init -> f196_0_reverse_NULL : arg1'=0, arg2'=arg2P_4, [ arg2P_5>0 && x3_1>-1 && 1+arg1P_1<=arg1P_5 && arg1P_5>0 && arg1P_1>-1 && arg1P_2<=arg1P_1 && -1+x3_1<1 && arg1P_2>0 ], cost: 3+arg1P_2 12: __init -> f196_0_reverse_NULL : arg1'=0, arg2'=arg2P_4, [ arg2P_5>0 && arg1P_5>0 && -1+x3_1>0 && arg1P_3>0 && -2+arg1P_3<=-1+arg1P_5 && arg1P_2<=arg1P_3 && arg1P_2>0 ], cost: 2+x3_1+arg1P_2 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 11: __init -> f196_0_reverse_NULL : arg1'=0, arg2'=arg2P_4, [ arg2P_5>0 && x3_1>-1 && 1+arg1P_1<=arg1P_5 && arg1P_5>0 && arg1P_1>-1 && arg1P_2<=arg1P_1 && -1+x3_1<1 && arg1P_2>0 ], cost: 3+arg1P_2 12: __init -> f196_0_reverse_NULL : arg1'=0, arg2'=arg2P_4, [ arg2P_5>0 && arg1P_5>0 && -1+x3_1>0 && arg1P_3>0 && -2+arg1P_3<=-1+arg1P_5 && arg1P_2<=arg1P_3 && arg1P_2>0 ], cost: 2+x3_1+arg1P_2 Computing asymptotic complexity for rule 11 Simplified the guard: 11: __init -> f196_0_reverse_NULL : arg1'=0, arg2'=arg2P_4, [ arg2P_5>0 && x3_1>-1 && 1+arg1P_1<=arg1P_5 && arg1P_5>0 && arg1P_2<=arg1P_1 && -1+x3_1<1 && arg1P_2>0 ], cost: 3+arg1P_2 Solved the limit problem by the following transformations: Created initial limit problem: 1+x3_1 (+/+!), arg2P_5 (+/+!), 2-x3_1 (+/+!), -arg1P_1+arg1P_5 (+/+!), 1+arg1P_1-arg1P_2 (+/+!), arg1P_5 (+/+!), 3+arg1P_2 (+), arg1P_2 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_1==2*n,arg2P_5==1,x3_1==0,arg1P_5==1+2*n,arg1P_2==n} resulting limit problem: [solved] Solution: arg1P_1 / 2*n arg2P_5 / 1 x3_1 / 0 arg1P_5 / 1+2*n arg1P_2 / 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_2 Rule guard: [ arg2P_5>0 && x3_1>-1 && 1+arg1P_1<=arg1P_5 && arg1P_5>0 && arg1P_2<=arg1P_1 && -1+x3_1<1 && arg1P_2>0 ] WORST_CASE(INF,?)