WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f180_0_ack_GT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && 0==arg2 && 0==arg1P_1 && 0==arg2P_1 ], cost: 1 1: f1_0_main_Load -> f180_0_ack_GT : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg2P_2>-1 && 1==arg2 && 0==arg1P_2 ], cost: 1 2: f1_0_main_Load -> f180_0_ack_GT : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3>-1 && arg2>1 && arg2P_3>-1 && arg1>0 ], cost: 1 3: f180_0_ack_GT -> f180_0_ack_GT : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>0 && -1+arg2 f180_0_ack_GT : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>0 && -1+arg20 && -1+arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1 5: f180_0_ack_GT -> f180_0_ack_GT : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>0 && arg2>0 && arg1P_6>0 && -1+arg2 f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f180_0_ack_GT : arg1'=0, arg2'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f180_0_ack_GT : arg1'=0, arg2'=arg2P_2, [ arg1>0 && arg2P_2>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f180_0_ack_GT : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3>-1 && arg2>1 && arg2P_3>-1 && arg1>0 ], cost: 1 3: f180_0_ack_GT -> f180_0_ack_GT : arg1'=1, arg2'=-1+arg2, [ arg2>0 && 0==arg1 ], cost: 1 4: f180_0_ack_GT -> f180_0_ack_GT : arg1'=-1+arg1, [ arg1>0 && arg2>0 ], cost: 1 5: f180_0_ack_GT -> f180_0_ack_GT : arg1'=arg1P_6, arg2'=-1+arg2, [ arg1>0 && arg2>0 && arg1P_6>0 ], cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 3: f180_0_ack_GT -> f180_0_ack_GT : arg1'=1, arg2'=-1+arg2, [ arg2>0 && 0==arg1 ], cost: 1 4: f180_0_ack_GT -> f180_0_ack_GT : arg1'=-1+arg1, [ arg1>0 && arg2>0 ], cost: 1 5: f180_0_ack_GT -> f180_0_ack_GT : arg1'=arg1P_6, arg2'=-1+arg2, [ arg1>0 && arg2>0 && arg1P_6>0 ], cost: 1 Accelerated rule 3 with metering function -arg1, yielding the new rule 7. Accelerated rule 4 with metering function arg1, yielding the new rule 8. Accelerated rule 5 with metering function arg2, yielding the new rule 9. During metering: Instantiating temporary variables by {arg1P_6==1} Removing the simple loops: 3 4 5. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f180_0_ack_GT : arg1'=0, arg2'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f180_0_ack_GT : arg1'=0, arg2'=arg2P_2, [ arg1>0 && arg2P_2>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f180_0_ack_GT : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3>-1 && arg2>1 && arg2P_3>-1 && arg1>0 ], cost: 1 7: f180_0_ack_GT -> f180_0_ack_GT : arg1'=1, arg2'=arg1+arg2, [ arg2>0 && 0==arg1 && -arg1>=1 ], cost: -arg1 8: f180_0_ack_GT -> f180_0_ack_GT : arg1'=0, [ arg1>0 && arg2>0 ], cost: arg1 9: f180_0_ack_GT -> f180_0_ack_GT : arg1'=arg1P_6, arg2'=0, [ arg1>0 && arg2>0 && arg1P_6>0 ], cost: arg2 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f180_0_ack_GT : arg1'=0, arg2'=0, [ arg1>0 && 0==arg2 ], cost: 1 1: f1_0_main_Load -> f180_0_ack_GT : arg1'=0, arg2'=arg2P_2, [ arg1>0 && arg2P_2>-1 && 1==arg2 ], cost: 1 2: f1_0_main_Load -> f180_0_ack_GT : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3>-1 && arg2>1 && arg2P_3>-1 && arg1>0 ], cost: 1 10: f1_0_main_Load -> f180_0_ack_GT : arg1'=0, arg2'=arg2P_3, [ arg2>1 && arg1>0 && arg1P_3>0 && arg2P_3>0 ], cost: 1+arg1P_3 11: f1_0_main_Load -> f180_0_ack_GT : arg1'=arg1P_6, arg2'=0, [ arg2>1 && arg1>0 && arg2P_3>0 && arg1P_6>0 ], cost: 1+arg2P_3 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 10: f1_0_main_Load -> f180_0_ack_GT : arg1'=0, arg2'=arg2P_3, [ arg2>1 && arg1>0 && arg1P_3>0 && arg2P_3>0 ], cost: 1+arg1P_3 11: f1_0_main_Load -> f180_0_ack_GT : arg1'=arg1P_6, arg2'=0, [ arg2>1 && arg1>0 && arg2P_3>0 && arg1P_6>0 ], cost: 1+arg2P_3 6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 12: __init -> f180_0_ack_GT : arg1'=0, arg2'=arg2P_3, [ arg2P_7>1 && arg1P_7>0 && arg1P_3>0 && arg2P_3>0 ], cost: 2+arg1P_3 13: __init -> f180_0_ack_GT : arg1'=arg1P_6, arg2'=0, [ arg2P_7>1 && arg1P_7>0 && arg2P_3>0 && arg1P_6>0 ], cost: 2+arg2P_3 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 12: __init -> f180_0_ack_GT : arg1'=0, arg2'=arg2P_3, [ arg2P_7>1 && arg1P_7>0 && arg1P_3>0 && arg2P_3>0 ], cost: 2+arg1P_3 13: __init -> f180_0_ack_GT : arg1'=arg1P_6, arg2'=0, [ arg2P_7>1 && arg1P_7>0 && arg2P_3>0 && arg1P_6>0 ], cost: 2+arg2P_3 Computing asymptotic complexity for rule 12 Solved the limit problem by the following transformations: Created initial limit problem: -1+arg2P_7 (+/+!), arg2P_3 (+/+!), arg1P_7 (+/+!), 2+arg1P_3 (+), arg1P_3 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg2P_3==n,arg1P_7==n,arg2P_7==n,arg1P_3==n} resulting limit problem: [solved] Solution: arg2P_3 / n arg1P_7 / n arg2P_7 / 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+arg1P_3 Rule guard: [ arg2P_7>1 && arg1P_7>0 && arg1P_3>0 && arg2P_3>0 ] WORST_CASE(INF,?)