WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 && 0==arg3P_1 ], cost: 1 1: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg4>-1 && arg3=-1+arg1P_2 && arg1>=arg2P_2 && arg2>=arg2P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && 2+arg4<=arg1 && 1+arg3==arg3P_2 && 1+arg4==arg4P_2 && arg5==arg5P_2 ], cost: 1 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_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, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 ], cost: 1 1: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3=-1+arg1P_2 && arg1>=arg2P_2 && arg2>=arg2P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && 2+arg4<=arg1 ], cost: 1 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f262_0_take_GE -> f262_0_take_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3=-1+arg1P_2 && arg1>=arg2P_2 && arg2>=arg2P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && 2+arg4<=arg1 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_2==1+arg1,arg2P_2==arg2} Accelerated rule 1 with metering function -arg3+arg5, yielding the new rule 3. Removing the simple loops: 1. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 ], cost: 1 3: f262_0_take_GE -> f262_0_take_GE : arg1'=-arg3+arg1+arg5, arg2'=arg2, arg3'=arg5, arg4'=-arg3+arg4+arg5, [ arg4>-1 && arg3=arg2 && arg1>0 && arg2>0 && 2+arg4<=arg1 ], cost: -arg3+arg5 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=arg4P_1, arg5'=arg5P_1, [ arg5P_1>-1 && arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 ], cost: 1 4: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1+arg5P_1, arg2'=arg2P_1, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 && 0=arg2P_1 && 2+arg4P_1<=arg1P_1 ], cost: 1+arg5P_1 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 4: f1_0_main_Load -> f262_0_take_GE : arg1'=arg1P_1+arg5P_1, arg2'=arg2P_1, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2>1 && arg4P_1>-1 && arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>0 && 0=arg2P_1 && 2+arg4P_1<=arg1P_1 ], cost: 1+arg5P_1 2: __init -> f1_0_main_Load : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 5: __init -> f262_0_take_GE : arg1'=arg1P_1+arg5P_1, arg2'=arg2P_1, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2P_3>1 && arg4P_1>-1 && arg2P_1<=arg1P_3 && arg1P_3>0 && arg1P_1>0 && arg2P_1>0 && 0=arg2P_1 && 2+arg4P_1<=arg1P_1 ], cost: 2+arg5P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 5: __init -> f262_0_take_GE : arg1'=arg1P_1+arg5P_1, arg2'=arg2P_1, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2P_3>1 && arg4P_1>-1 && arg2P_1<=arg1P_3 && arg1P_3>0 && arg1P_1>0 && arg2P_1>0 && 0=arg2P_1 && 2+arg4P_1<=arg1P_1 ], cost: 2+arg5P_1 Computing asymptotic complexity for rule 5 Simplified the guard: 5: __init -> f262_0_take_GE : arg1'=arg1P_1+arg5P_1, arg2'=arg2P_1, arg3'=arg5P_1, arg4'=arg4P_1+arg5P_1, arg5'=arg5P_1, [ arg2P_3>1 && arg4P_1>-1 && arg2P_1<=arg1P_3 && arg1P_3>0 && arg2P_1>0 && 0=arg2P_1 && 2+arg4P_1<=arg1P_1 ], cost: 2+arg5P_1 Solved the limit problem by the following transformations: Created initial limit problem: -1+arg2P_3 (+/+!), arg2P_1 (+/+!), -1+arg1P_1-arg4P_1 (+/+!), 1-arg2P_1+arg1P_3 (+/+!), arg1P_3 (+/+!), 2+arg5P_1 (+), arg5P_1 (+/+!), 1+arg4P_1 (+/+!), 1-arg2P_1+arg1P_1 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg2P_1==1,arg2P_3==n,arg1P_1==2,arg1P_3==1,arg4P_1==0,arg5P_1==n} resulting limit problem: [solved] Solution: arg2P_1 / 1 arg2P_3 / n arg1P_1 / 2 arg1P_3 / 1 arg4P_1 / 0 arg5P_1 / 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+arg5P_1 Rule guard: [ arg2P_3>1 && arg4P_1>-1 && arg2P_1<=arg1P_3 && arg1P_3>0 && arg2P_1>0 && 0=arg2P_1 && 2+arg4P_1<=arg1P_1 ] WORST_CASE(INF,?)