WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f191_0_main_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1>0 && arg2>-1 && -1+arg2==arg1P_1 && arg2==arg2P_1 && 0==arg3P_1 ], cost: 1 1: f191_0_main_LE -> f191_0_main_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>0 && arg3>0 && -1+arg1==arg1P_2 && arg1==arg2P_2 ], cost: 1 2: f191_0_main_LE -> f191_0_main_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && -1+arg1==arg1P_3 && arg1==arg2P_3 && 1==arg3P_3 ], cost: 1 3: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2<1 && arg1P_4>0 ], cost: 1 4: f270_0_length_FieldAccess -> f270_0_length_FieldAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ 1+arg1P_5<=arg1 && arg1>0 && arg1P_5>-1 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f191_0_main_LE : arg1'=-1+arg2, arg3'=0, [ arg1>0 && arg2>-1 ], cost: 1 1: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=arg3P_2, [ arg2>0 && arg3>0 ], cost: 1 2: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=1, [ arg2>0 ], cost: 1 3: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2<1 && arg1P_4>0 ], cost: 1 4: f270_0_length_FieldAccess -> f270_0_length_FieldAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ 1+arg1P_5<=arg1 && arg1>0 && arg1P_5>-1 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=arg3P_2, [ arg2>0 && arg3>0 ], cost: 1 2: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=1, [ arg2>0 ], cost: 1 Found no metering function for rule 1. Found no metering function for rule 2. Removing the simple loops:. Accelerating simple loops of location 2. Accelerating the following rules: 4: f270_0_length_FieldAccess -> f270_0_length_FieldAccess : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ 1+arg1P_5<=arg1 && arg1>0 && arg1P_5>-1 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_5==-1+arg1} Accelerated rule 4 with metering function arg1, yielding the new rule 6. Removing the simple loops: 4. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f191_0_main_LE : arg1'=-1+arg2, arg3'=0, [ arg1>0 && arg2>-1 ], cost: 1 1: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=arg3P_2, [ arg2>0 && arg3>0 ], cost: 1 2: f191_0_main_LE -> f191_0_main_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=1, [ arg2>0 ], cost: 1 3: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2<1 && arg1P_4>0 ], cost: 1 6: f270_0_length_FieldAccess -> f270_0_length_FieldAccess : arg1'=0, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1>0 ], cost: arg1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f191_0_main_LE : arg1'=-1+arg2, arg3'=0, [ arg1>0 && arg2>-1 ], cost: 1 7: f1_0_main_Load -> f191_0_main_LE : arg1'=-2+arg2, arg2'=-1+arg2, arg3'=1, [ arg1>0 && arg2>0 ], cost: 2 3: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2<1 && arg1P_4>0 ], cost: 1 8: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=0, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2<1 && arg1P_4>0 ], cost: 1+arg1P_4 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f191_0_main_LE : arg1'=-1+arg2, arg3'=0, [ arg1>0 && arg2>-1 ], cost: 1 7: f1_0_main_Load -> f191_0_main_LE : arg1'=-2+arg2, arg2'=-1+arg2, arg3'=1, [ arg1>0 && arg2>0 ], cost: 2 8: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=0, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2<1 && arg1P_4>0 ], cost: 1+arg1P_4 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 8: f191_0_main_LE -> f270_0_length_FieldAccess : arg1'=0, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2<1 && arg1P_4>0 ], cost: 1+arg1P_4 9: __init -> f191_0_main_LE : arg1'=-1+arg2P_6, arg2'=arg2P_6, arg3'=0, [ arg1P_6>0 && arg2P_6>-1 ], cost: 2 10: __init -> f191_0_main_LE : arg1'=-2+arg2P_6, arg2'=-1+arg2P_6, arg3'=1, [ arg1P_6>0 && arg2P_6>0 ], cost: 3 Eliminated locations (on tree-shaped paths): Start location: __init 11: __init -> f270_0_length_FieldAccess : arg1'=0, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_6>0 && arg2P_6>-1 && arg2P_6<1 && arg1P_4>0 ], cost: 3+arg1P_4 12: __init -> f270_0_length_FieldAccess : arg1'=0, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_6>0 && arg2P_6>0 && -1+arg2P_6<1 && arg1P_4>0 ], cost: 4+arg1P_4 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 11: __init -> f270_0_length_FieldAccess : arg1'=0, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_6>0 && arg2P_6>-1 && arg2P_6<1 && arg1P_4>0 ], cost: 3+arg1P_4 12: __init -> f270_0_length_FieldAccess : arg1'=0, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_6>0 && arg2P_6>0 && -1+arg2P_6<1 && arg1P_4>0 ], cost: 4+arg1P_4 Computing asymptotic complexity for rule 11 Solved the limit problem by the following transformations: Created initial limit problem: arg1P_6 (+/+!), arg1P_4 (+/+!), 1+arg2P_6 (+/+!), 1-arg2P_6 (+/+!), 3+arg1P_4 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_6==n,arg1P_4==n,arg2P_6==0} resulting limit problem: [solved] Solution: arg1P_6 / n arg1P_4 / n arg2P_6 / 0 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_4 Rule guard: [ arg1P_6>0 && arg2P_6>-1 && arg2P_6<1 && arg1P_4>0 ] WORST_CASE(INF,?)