WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 && 2==arg3P_1 ], cost: 1 1: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1>-1 && -1==arg2 && -1+arg1==arg1P_2 && -1==arg2P_2 && arg3==arg3P_2 ], cost: 1 2: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1P_3>-1 && arg2>-1 && arg3>-1 && -1+arg2==arg2P_3 && 1+arg3==arg3P_3 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=2, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1 1: f339_0_main_LT -> f339_0_main_LT : arg1'=-1+arg1, arg2'=-1, [ arg1>-1 && -1==arg2 ], cost: 1 2: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P_3, arg2'=-1+arg2, arg3'=1+arg3, [ arg1P_3>-1 && arg2>-1 && arg3>-1 ], cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f339_0_main_LT -> f339_0_main_LT : arg1'=-1+arg1, arg2'=-1, [ arg1>-1 && -1==arg2 ], cost: 1 2: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P_3, arg2'=-1+arg2, arg3'=1+arg3, [ arg1P_3>-1 && arg2>-1 && arg3>-1 ], cost: 1 Accelerated rule 1 with metering function 1+arg1, yielding the new rule 4. Accelerated rule 2 with metering function 1+arg2, yielding the new rule 5. Nested simple loops 2 (outer loop) and 4 (inner loop) with metering function 1+arg2, resulting in the new rules: 6. Removing the simple loops: 1 2. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=2, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1 4: f339_0_main_LT -> f339_0_main_LT : arg1'=-1, arg2'=-1, [ arg1>-1 && -1==arg2 ], cost: 1+arg1 5: f339_0_main_LT -> f339_0_main_LT : arg1'=arg1P_3, arg2'=-1, arg3'=1+arg3+arg2, [ arg1P_3>-1 && arg2>-1 && arg3>-1 ], cost: 1+arg2 6: f339_0_main_LT -> f339_0_main_LT : arg1'=-1, arg2'=-1, arg3'=1+arg3+arg2, [ arg1P_3>-1 && arg3>-1 && -1==-1+arg2 ], cost: 2+arg1P_3*(1+arg2)+2*arg2 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=2, [ arg1P_1>-1 && arg2>-1 && arg2P_1>-1 && arg1>0 ], cost: 1 7: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P_3, arg2'=-1, arg3'=3+arg2P_1, [ arg2>-1 && arg2P_1>-1 && arg1>0 && arg1P_3>-1 ], cost: 2+arg2P_1 8: f1_0_main_Load -> f339_0_main_LT : arg1'=-1, arg2'=-1, arg3'=3, [ arg2>-1 && arg1>0 && arg1P_3>-1 ], cost: 3+arg1P_3 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 7: f1_0_main_Load -> f339_0_main_LT : arg1'=arg1P_3, arg2'=-1, arg3'=3+arg2P_1, [ arg2>-1 && arg2P_1>-1 && arg1>0 && arg1P_3>-1 ], cost: 2+arg2P_1 8: f1_0_main_Load -> f339_0_main_LT : arg1'=-1, arg2'=-1, arg3'=3, [ arg2>-1 && arg1>0 && arg1P_3>-1 ], cost: 3+arg1P_3 3: __init -> f1_0_main_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 9: __init -> f339_0_main_LT : arg1'=arg1P_3, arg2'=-1, arg3'=3+arg2P_1, [ arg2P_4>-1 && arg2P_1>-1 && arg1P_4>0 && arg1P_3>-1 ], cost: 3+arg2P_1 10: __init -> f339_0_main_LT : arg1'=-1, arg2'=-1, arg3'=3, [ arg2P_4>-1 && arg1P_4>0 && arg1P_3>-1 ], cost: 4+arg1P_3 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 9: __init -> f339_0_main_LT : arg1'=arg1P_3, arg2'=-1, arg3'=3+arg2P_1, [ arg2P_4>-1 && arg2P_1>-1 && arg1P_4>0 && arg1P_3>-1 ], cost: 3+arg2P_1 10: __init -> f339_0_main_LT : arg1'=-1, arg2'=-1, arg3'=3, [ arg2P_4>-1 && arg1P_4>0 && arg1P_3>-1 ], cost: 4+arg1P_3 Computing asymptotic complexity for rule 9 Solved the limit problem by the following transformations: Created initial limit problem: 1+arg1P_3 (+/+!), arg1P_4 (+/+!), 1+arg2P_1 (+/+!), 1+arg2P_4 (+/+!), 3+arg2P_1 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_4==n,arg1P_3==n,arg2P_4==n,arg2P_1==n} resulting limit problem: [solved] Solution: arg1P_4 / n arg1P_3 / n arg2P_4 / n arg2P_1 / 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+arg2P_1 Rule guard: [ arg2P_4>-1 && arg2P_1>-1 && arg1P_4>0 && arg1P_3>-1 ] WORST_CASE(INF,?)