/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),a()),x) -> f#(a(),x)
   f#(f(a(),a()),x) -> f#(b(),f(a(),x))
   f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
   f#(x,f(y,z)) -> f#(x,y)
   f#(x,f(y,z)) -> f#(f(x,y),z)
  TRS:
   f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
   f(x,f(y,z)) -> f(f(x,y),z)
  EDG Processor:
   DPs:
    f#(f(a(),a()),x) -> f#(a(),x)
    f#(f(a(),a()),x) -> f#(b(),f(a(),x))
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
    f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(f(x,y),z)
   TRS:
    f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
    f(x,f(y,z)) -> f(f(x,y),z)
   graph:
    f#(f(a(),a()),x) -> f#(b(),f(a(),x)) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),a()),x) -> f#(b(),f(a(),x)) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x))) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x))) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(a(),a()),x) -> f#(a(),x) -> f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),a()),x) -> f#(a(),x) -> f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(f(a(),a()),x) -> f#(a(),x)
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(a(),a()),x) -> f#(b(),f(a(),x))
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),a()),x) -> f#(a(),x)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),a()),x) -> f#(b(),f(a(),x))
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
    f#(x,f(y,z)) -> f#(x,y) -> f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(x,y) -> f#(x,f(y,z)) -> f#(f(x,y),z)
   Semantic Labeling Processor:
    dimension: 1
    usable rules:
     f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
     f(x,f(y,z)) -> f(f(x,y),z)
    interpretation:
     [b] = 1,
     
     [f](x0, x1) = x0 + 1,
     
     [a] = 1
     labeled:
      a
      b
     usable (for model):
      a
      b
     argument filtering:
      pi(a) = []
      pi(f) = 0
      pi(b) = []
      pi(f#) = 0
    precedence:
     a > f# ~ b ~ f
    problem:
     DPs:
      f#(f(a(),a()),x) -> f#(a(),x)
      f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
      f#(x,f(y,z)) -> f#(x,y)
      f#(x,f(y,z)) -> f#(f(x,y),z)
     TRS:
      f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
      f(x,f(y,z)) -> f(f(x,y),z)
    Restore Modifier:
     DPs:
      f#(f(a(),a()),x) -> f#(a(),x)
      f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
      f#(x,f(y,z)) -> f#(x,y)
      f#(x,f(y,z)) -> f#(f(x,y),z)
     TRS:
      f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
      f(x,f(y,z)) -> f(f(x,y),z)
     Matrix Interpretation Processor: dim=1
      
      usable rules:
       f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
       f(x,f(y,z)) -> f(f(x,y),z)
      interpretation:
       [f#](x0, x1) = 2x0 + 2x1,
       
       [b] = 0,
       
       [f](x0, x1) = x0 + x1,
       
       [a] = 1
      orientation:
       f#(f(a(),a()),x) = 2x + 4 >= 2x + 2 = f#(a(),x)
       
       f#(f(a(),a()),x) = 2x + 4 >= 2x + 4 = f#(a(),f(b(),f(a(),x)))
       
       f#(x,f(y,z)) = 2x + 2y + 2z >= 2x + 2y = f#(x,y)
       
       f#(x,f(y,z)) = 2x + 2y + 2z >= 2x + 2y + 2z = f#(f(x,y),z)
       
       f(f(a(),a()),x) = x + 2 >= x + 2 = f(a(),f(b(),f(a(),x)))
       
       f(x,f(y,z)) = x + y + z >= x + y + z = f(f(x,y),z)
      problem:
       DPs:
        f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
        f#(x,f(y,z)) -> f#(x,y)
        f#(x,f(y,z)) -> f#(f(x,y),z)
       TRS:
        f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
        f(x,f(y,z)) -> f(f(x,y),z)
      Restore Modifier:
       DPs:
        f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
        f#(x,f(y,z)) -> f#(x,y)
        f#(x,f(y,z)) -> f#(f(x,y),z)
       TRS:
        f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
        f(x,f(y,z)) -> f(f(x,y),z)
       Bounds Processor:
        bound: 0
        enrichment: match-dp
        automaton:
         final states: {1}
         transitions:
          f220() -> 2*
          f{#,0}(3,5) -> 1*
          f{#,0}(24,2) -> 1*
          f{#,0}(19,4) -> 1*
          f{#,0}(24,6) -> 1*
          f{#,0}(24,20) -> 1*
          f{#,0}(3,6) -> 1*
          f{#,0}(19,3) -> 1*
          f{#,0}(3,20) -> 1*
          f{#,0}(24,5) -> 1*
          f{#,0}(19,19) -> 1*
          a0() -> 3*
          f0(3,5) -> 19*
          f0(24,2) -> 24*
          f0(19,4) -> 24*
          f0(24,6) -> 24,4
          f0(4,2) -> 4*
          f0(24,20) -> 24,4
          f0(20,5) -> 5*
          f0(5,3) -> 6,20
          f0(5,19) -> 5*
          f0(6,2) -> 6*
          f0(6,6) -> 6*
          f0(6,20) -> 6*
          f0(3,2) -> 4*
          f0(3,6) -> 24*
          f0(19,3) -> 24*
          f0(3,20) -> 24*
          f0(24,5) -> 19*
          f0(19,19) -> 19*
          f0(20,2) -> 6*
          f0(20,6) -> 6*
          f0(5,4) -> 6*
          f0(20,20) -> 6*
          f0(6,5) -> 5*
          b0() -> 5*
          24 -> 4*
        problem:
         DPs:
          f#(x,f(y,z)) -> f#(x,y)
          f#(x,f(y,z)) -> f#(f(x,y),z)
         TRS:
          f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
          f(x,f(y,z)) -> f(f(x,y),z)
        Size-Change Termination Processor:
         DPs:
          
         TRS:
          f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
          f(x,f(y,z)) -> f(f(x,y),z)
         The DP: f#(x,f(y,z)) -> f#(x,y) has the edges:
           0 >=  0
           1 >   1
         The DP: f#(x,f(y,z)) -> f#(f(x,y),z) has the edges:
           1 >   1
         Qed