WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f142_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1 1: f142_0_main_LE -> f153_0_main_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>0 && arg2==arg1P_2 && arg1==arg2P_2 ], cost: 1 2: f153_0_main_LE -> f142_0_main_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ 0==arg2 && 0==arg1P_3 && -1+arg1==arg2P_3 ], cost: 1 3: f153_0_main_LE -> f153_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>0 && arg1==arg1P_4 && -1+arg2==arg2P_4 ], 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 -> f142_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1 1: f142_0_main_LE -> f153_0_main_LE : arg1'=arg2, arg2'=arg1, [ arg2>0 ], cost: 1 2: f153_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=-1+arg1, [ 0==arg2 ], cost: 1 3: f153_0_main_LE -> f153_0_main_LE : arg2'=-1+arg2, [ arg2>0 ], 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 2. Accelerating the following rules: 3: f153_0_main_LE -> f153_0_main_LE : arg2'=-1+arg2, [ arg2>0 ], cost: 1 Accelerated rule 3 with metering function arg2, yielding the new rule 5. Removing the simple loops: 3. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f142_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1 1: f142_0_main_LE -> f153_0_main_LE : arg1'=arg2, arg2'=arg1, [ arg2>0 ], cost: 1 2: f153_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=-1+arg1, [ 0==arg2 ], cost: 1 5: f153_0_main_LE -> f153_0_main_LE : arg2'=0, [ arg2>0 ], cost: arg2 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 -> f142_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1 1: f142_0_main_LE -> f153_0_main_LE : arg1'=arg2, arg2'=arg1, [ arg2>0 ], cost: 1 6: f142_0_main_LE -> f153_0_main_LE : arg1'=arg2, arg2'=0, [ arg2>0 && arg1>0 ], cost: 1+arg1 2: f153_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=-1+arg1, [ 0==arg2 ], cost: 1 4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 1: f142_0_main_LE -> f153_0_main_LE : arg1'=arg2, arg2'=arg1, [ arg2>0 ], cost: 1 6: f142_0_main_LE -> f153_0_main_LE : arg1'=arg2, arg2'=0, [ arg2>0 && arg1>0 ], cost: 1+arg1 2: f153_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=-1+arg1, [ 0==arg2 ], cost: 1 7: __init -> f142_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1>-1 && arg2P_5>-1 && arg2P_1>-1 && arg1P_5>0 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 8: f142_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=-1+arg2, [ arg2>0 && 0==arg1 ], cost: 2 9: f142_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=-1+arg2, [ arg2>0 && arg1>0 ], cost: 2+arg1 7: __init -> f142_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1>-1 && arg2P_5>-1 && arg2P_1>-1 && arg1P_5>0 ], cost: 2 Accelerating simple loops of location 1. Accelerating the following rules: 8: f142_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=-1+arg2, [ arg2>0 && 0==arg1 ], cost: 2 9: f142_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=-1+arg2, [ arg2>0 && arg1>0 ], cost: 2+arg1 Accelerated rule 8 with metering function arg2, yielding the new rule 10. Found no metering function for rule 9. Removing the simple loops: 8. Accelerated all simple loops using metering functions (where possible): Start location: __init 9: f142_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=-1+arg2, [ arg2>0 && arg1>0 ], cost: 2+arg1 10: f142_0_main_LE -> f142_0_main_LE : arg1'=0, arg2'=0, [ arg2>0 && 0==arg1 ], cost: 2*arg2 7: __init -> f142_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1>-1 && arg2P_5>-1 && arg2P_1>-1 && arg1P_5>0 ], cost: 2 Chained accelerated rules (with incoming rules): Start location: __init 7: __init -> f142_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1>-1 && arg2P_5>-1 && arg2P_1>-1 && arg1P_5>0 ], cost: 2 11: __init -> f142_0_main_LE : arg1'=0, arg2'=-1+arg2P_1, [ arg2P_1>0 && arg1P_1>0 ], cost: 4+arg1P_1 12: __init -> f142_0_main_LE : arg1'=0, arg2'=0, [ arg2P_1>0 ], cost: 2+2*arg2P_1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 11: __init -> f142_0_main_LE : arg1'=0, arg2'=-1+arg2P_1, [ arg2P_1>0 && arg1P_1>0 ], cost: 4+arg1P_1 12: __init -> f142_0_main_LE : arg1'=0, arg2'=0, [ arg2P_1>0 ], cost: 2+2*arg2P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 11: __init -> f142_0_main_LE : arg1'=0, arg2'=-1+arg2P_1, [ arg2P_1>0 && arg1P_1>0 ], cost: 4+arg1P_1 12: __init -> f142_0_main_LE : arg1'=0, arg2'=0, [ arg2P_1>0 ], cost: 2+2*arg2P_1 Computing asymptotic complexity for rule 11 Solved the limit problem by the following transformations: Created initial limit problem: arg2P_1 (+/+!), 4+arg1P_1 (+), arg1P_1 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg2P_1==1,arg1P_1==n} resulting limit problem: [solved] Solution: arg2P_1 / 1 arg1P_1 / n Resulting cost 4+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: 4+n Rule cost: 4+arg1P_1 Rule guard: [ arg2P_1>0 && arg1P_1>0 ] WORST_CASE(INF,?)