WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f145_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f145_0_main_LE -> f145_0_main_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2 f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f145_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f145_0_main_LE -> f145_0_main_LE : arg1'=-1+arg1, arg2'=1+arg2, [ arg2 f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f145_0_main_LE -> f145_0_main_LE : arg1'=-1+arg1, arg2'=1+arg2, [ arg2 f145_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1 3: f145_0_main_LE -> f145_0_main_LE : arg1'=-meter+arg1, arg2'=meter+arg2, [ arg2=1 ], cost: meter 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f145_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1 4: f1_0_main_Load -> f145_0_main_LE : arg1'=-meter+arg1P_1, arg2'=-meter+arg1P_1, [ -2*meter+arg1P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 && -2*meter+arg1P_1=1 ], cost: 1+meter 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 4: f1_0_main_Load -> f145_0_main_LE : arg1'=-meter+arg1P_1, arg2'=-meter+arg1P_1, [ -2*meter+arg1P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 && -2*meter+arg1P_1=1 ], cost: 1+meter 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 5: __init -> f145_0_main_LE : arg1'=-meter+arg1P_1, arg2'=-meter+arg1P_1, [ -2*meter+arg1P_1>-1 && arg2P_3>-1 && arg1P_1>-1 && arg1P_3>0 && -2*meter+arg1P_1=1 ], cost: 2+meter ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 5: __init -> f145_0_main_LE : arg1'=-meter+arg1P_1, arg2'=-meter+arg1P_1, [ -2*meter+arg1P_1>-1 && arg2P_3>-1 && arg1P_1>-1 && arg1P_3>0 && -2*meter+arg1P_1=1 ], cost: 2+meter Computing asymptotic complexity for rule 5 Solved the limit problem by the following transformations: Created initial limit problem: 1+arg1P_1 (+/+!), 2+meter (+), 1-2*meter+arg1P_1 (+/+!), 1+arg2P_3 (+/+!), arg1P_3 (+/+!), 2*meter (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter==n,arg2P_3==n,arg1P_1==2*n,arg1P_3==n} resulting limit problem: [solved] Solution: meter / n arg2P_3 / n arg1P_1 / 2*n arg1P_3 / 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: 2+meter Rule guard: [ -2*meter+arg1P_1>-1 && arg2P_3>-1 && arg1P_1>-1 && arg1P_3>0 && -2*meter+arg1P_1