/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 f(y,f(y,x)) -> f(f(a(),y),f(a(),y))

Proof:
 DP Processor:
  DPs:
   f#(y,f(y,x)) -> f#(a(),y)
   f#(y,f(y,x)) -> f#(f(a(),y),f(a(),y))
  TRS:
   f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
  Arctic Interpretation Processor:
   dimension: 1
   usable rules:
    f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
   interpretation:
    [a] = 0,
    
    [f](x0, x1) = 1x0 + 1x1 + 4,
    
    [f#](x0, x1) = x0 + x1 + 0
   orientation:
    f#(y,f(y,x)) = 1x + 1y + 4 >= y + 0 = f#(a(),y)
    
    f#(y,f(y,x)) = 1x + 1y + 4 >= 1y + 4 = f#(f(a(),y),f(a(),y))
    
    f(y,f(y,x)) = 2x + 2y + 5 >= 2y + 5 = f(f(a(),y),f(a(),y))
   problem:
    DPs:
     f#(y,f(y,x)) -> f#(f(a(),y),f(a(),y))
    TRS:
     f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
   Restore Modifier:
    DPs:
     f#(y,f(y,x)) -> f#(f(a(),y),f(a(),y))
    TRS:
     f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
    Bounds Processor:
     bound: 2
     enrichment: match-dp
     automaton:
      final states: {3}
      transitions:
       f{#,1}(1,1) -> 3*
       f{#,1}(24,24) -> 3*
       f{#,1}(35,1) -> 3*
       f{#,1}(35,24) -> 3*
       f{#,1}(24,35) -> 3*
       f{#,1}(24,1) -> 3*
       f{#,1}(1,24) -> 3*
       f{#,1}(1,35) -> 3*
       f{#,1}(35,35) -> 3*
       f{#,0}(1,2) -> 3*
       f{#,0}(2,1) -> 3*
       f{#,0}(22,22) -> 3*
       f{#,0}(2,2) -> 3*
       f{#,0}(22,1) -> 3*
       f{#,0}(22,35) -> 3*
       f{#,0}(2,22) -> 3*
       f{#,0}(24,22) -> 3*
       f{#,0}(35,2) -> 3*
       f{#,0}(24,2) -> 3*
       f{#,0}(2,35) -> 3*
       f{#,0}(22,24) -> 3*
       f{#,0}(22,2) -> 3*
       f{#,0}(1,22) -> 3*
       f{#,0}(2,24) -> 3*
       f{#,0}(35,22) -> 3*
       f1(22,22) -> 1*
       f1(22,2) -> 1*
       f1(22,24) -> 1*
       f1(2,35) -> 1*
       f1(2,1) -> 1*
       f1(22,35) -> 1*
       f1(24,1) -> 1*
       f1(1,35) -> 1*
       f1(24,24) -> 1*
       f1(2,24) -> 1*
       f1(35,24) -> 1*
       f1(22,1) -> 1*
       f1(1,1) -> 1*
       f1(35,35) -> 1*
       f1(2,22) -> 1*
       f1(24,35) -> 1*
       f1(2,2) -> 1*
       f1(35,1) -> 1*
       f1(1,24) -> 1*
       f0(35,2) -> 1*
       f0(1,2) -> 1*
       f0(24,22) -> 1*
       f0(1,22) -> 1*
       f0(24,2) -> 1*
       f0(35,22) -> 1*
       f{#,2}(23,19) -> 3*
       f{#,2}(23,23) -> 3*
       f{#,2}(21,24) -> 3*
       f{#,2}(23,24) -> 3*
       f{#,2}(24,19) -> 3*
       f{#,2}(24,24) -> 3*
       f{#,2}(21,23) -> 3*
       f{#,2}(21,19) -> 3*
       f{#,2}(24,23) -> 3*
       a2() -> 22*,2,20,18
       f2(20,35) -> 21*
       f2(20,1) -> 21*
       f2(18,24) -> 19*
       f2(35,25) -> 24*
       f2(22,35) -> 1,21,24*,19
       f2(20,24) -> 21*
       f2(22,24) -> 1,21,24*,19
       f2(26,35) -> 24*
       f2(26,25) -> 24*
       f2(22,1) -> 23,24*,1,21,19
       f2(35,35) -> 1,24*
       f2(22,22) -> 35*,1,26,25
       f2(18,35) -> 19*
       f2(18,1) -> 19*
     problem:
      DPs:
       
      TRS:
       f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
     Qed