/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(a(),f(a(),x)) -> f(c(),f(b(),x))
 f(b(),f(b(),x)) -> f(a(),f(c(),x))
 f(c(),f(c(),x)) -> f(b(),f(a(),x))

Proof:
 Extended Uncurrying Processor:
  application symbol: f
  symbol table:
   b ==> b0/0 b1/1
   c ==> c0/0 c1/1
   a ==> a0/0 a1/1
   
  uncurry-rules:
   f(a0(),x1) -> a1(x1)
   f(c0(),x3) -> c1(x3)
   f(b0(),x5) -> b1(x5)
  eta-rules:
   
  problem:
   a1(a1(x)) -> c1(b1(x))
   b1(b1(x)) -> a1(c1(x))
   c1(c1(x)) -> b1(a1(x))
   f(a0(),x1) -> a1(x1)
   f(c0(),x3) -> c1(x3)
   f(b0(),x5) -> b1(x5)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a0] = 0,
    
    [b0] = 1,
    
    [f](x0, x1) = 5x0 + 3x1,
    
    [a1](x0) = 3x0,
    
    [c1](x0) = 3x0,
    
    [b1](x0) = 3x0,
    
    [c0] = 0
   orientation:
    a1(a1(x)) = 9x >= 9x = c1(b1(x))
    
    b1(b1(x)) = 9x >= 9x = a1(c1(x))
    
    c1(c1(x)) = 9x >= 9x = b1(a1(x))
    
    f(a0(),x1) = 3x1 >= 3x1 = a1(x1)
    
    f(c0(),x3) = 3x3 >= 3x3 = c1(x3)
    
    f(b0(),x5) = 3x5 + 5 >= 3x5 = b1(x5)
   problem:
    a1(a1(x)) -> c1(b1(x))
    b1(b1(x)) -> a1(c1(x))
    c1(c1(x)) -> b1(a1(x))
    f(a0(),x1) -> a1(x1)
    f(c0(),x3) -> c1(x3)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [a0] = 0,
     
     [f](x0, x1) = 3x0 + 2x1 + 4,
     
     [a1](x0) = 2x0 + 4,
     
     [c1](x0) = 2x0 + 4,
     
     [b1](x0) = 2x0 + 4,
     
     [c0] = 3
    orientation:
     a1(a1(x)) = 4x + 12 >= 4x + 12 = c1(b1(x))
     
     b1(b1(x)) = 4x + 12 >= 4x + 12 = a1(c1(x))
     
     c1(c1(x)) = 4x + 12 >= 4x + 12 = b1(a1(x))
     
     f(a0(),x1) = 2x1 + 4 >= 2x1 + 4 = a1(x1)
     
     f(c0(),x3) = 2x3 + 13 >= 2x3 + 4 = c1(x3)
    problem:
     a1(a1(x)) -> c1(b1(x))
     b1(b1(x)) -> a1(c1(x))
     c1(c1(x)) -> b1(a1(x))
     f(a0(),x1) -> a1(x1)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
             [1]
      [a0] = [0]
             [0],
      
                    [1 0 0]     [1 1 1]  
      [f](x0, x1) = [1 0 0]x0 + [0 1 0]x1
                    [0 0 0]     [1 1 0]  ,
      
                 [1 0 0]  
      [a1](x0) = [0 0 0]x0
                 [0 0 0]  ,
      
                 [1 0 0]  
      [c1](x0) = [0 0 0]x0
                 [0 0 0]  ,
      
                 [1 0 0]  
      [b1](x0) = [0 0 0]x0
                 [0 0 0]  
     orientation:
                  [1 0 0]     [1 0 0]             
      a1(a1(x)) = [0 0 0]x >= [0 0 0]x = c1(b1(x))
                  [0 0 0]     [0 0 0]             
      
                  [1 0 0]     [1 0 0]             
      b1(b1(x)) = [0 0 0]x >= [0 0 0]x = a1(c1(x))
                  [0 0 0]     [0 0 0]             
      
                  [1 0 0]     [1 0 0]             
      c1(c1(x)) = [0 0 0]x >= [0 0 0]x = b1(a1(x))
                  [0 0 0]     [0 0 0]             
      
                   [1 1 1]     [1]    [1 0 0]           
      f(a0(),x1) = [0 1 0]x1 + [1] >= [0 0 0]x1 = a1(x1)
                   [1 1 0]     [0]    [0 0 0]           
     problem:
      a1(a1(x)) -> c1(b1(x))
      b1(b1(x)) -> a1(c1(x))
      c1(c1(x)) -> b1(a1(x))
     DP Processor:
      DPs:
       a{1,#}(a1(x)) -> b{1,#}(x)
       a{1,#}(a1(x)) -> c{1,#}(b1(x))
       b{1,#}(b1(x)) -> c{1,#}(x)
       b{1,#}(b1(x)) -> a{1,#}(c1(x))
       c{1,#}(c1(x)) -> a{1,#}(x)
       c{1,#}(c1(x)) -> b{1,#}(a1(x))
      TRS:
       a1(a1(x)) -> c1(b1(x))
       b1(b1(x)) -> a1(c1(x))
       c1(c1(x)) -> b1(a1(x))
      TDG Processor:
       DPs:
        a{1,#}(a1(x)) -> b{1,#}(x)
        a{1,#}(a1(x)) -> c{1,#}(b1(x))
        b{1,#}(b1(x)) -> c{1,#}(x)
        b{1,#}(b1(x)) -> a{1,#}(c1(x))
        c{1,#}(c1(x)) -> a{1,#}(x)
        c{1,#}(c1(x)) -> b{1,#}(a1(x))
       TRS:
        a1(a1(x)) -> c1(b1(x))
        b1(b1(x)) -> a1(c1(x))
        c1(c1(x)) -> b1(a1(x))
       graph:
        c{1,#}(c1(x)) -> b{1,#}(a1(x)) ->
        b{1,#}(b1(x)) -> a{1,#}(c1(x))
        c{1,#}(c1(x)) -> b{1,#}(a1(x)) -> b{1,#}(b1(x)) -> c{1,#}(x)
        c{1,#}(c1(x)) -> a{1,#}(x) -> a{1,#}(a1(x)) -> c{1,#}(b1(x))
        c{1,#}(c1(x)) -> a{1,#}(x) -> a{1,#}(a1(x)) -> b{1,#}(x)
        b{1,#}(b1(x)) -> c{1,#}(x) -> c{1,#}(c1(x)) -> b{1,#}(a1(x))
        b{1,#}(b1(x)) -> c{1,#}(x) -> c{1,#}(c1(x)) -> a{1,#}(x)
        b{1,#}(b1(x)) -> a{1,#}(c1(x)) ->
        a{1,#}(a1(x)) -> c{1,#}(b1(x))
        b{1,#}(b1(x)) -> a{1,#}(c1(x)) -> a{1,#}(a1(x)) -> b{1,#}(x)
        a{1,#}(a1(x)) -> c{1,#}(b1(x)) ->
        c{1,#}(c1(x)) -> b{1,#}(a1(x))
        a{1,#}(a1(x)) -> c{1,#}(b1(x)) -> c{1,#}(c1(x)) -> a{1,#}(x)
        a{1,#}(a1(x)) -> b{1,#}(x) -> b{1,#}(b1(x)) -> a{1,#}(c1(x))
        a{1,#}(a1(x)) -> b{1,#}(x) -> b{1,#}(b1(x)) -> c{1,#}(x)
       Bounds Processor:
        bound: 0
        enrichment: match
        automaton:
         final states: {13,12,11,9,8,6,5,3,1}
         transitions:
          a{1,0}(7) -> 12*
          a{1,0}(2) -> 10*
          f130() -> 2*
          c{1,#,0}(2) -> 5*
          c{1,#,0}(4) -> 3*
          b{1,0}(2) -> 4*
          b{1,0}(10) -> 13*
          c{1,0}(4) -> 11*
          c{1,0}(2) -> 7*
          a{1,#,0}(7) -> 6*
          a{1,#,0}(2) -> 8*
          b{1,#,0}(10) -> 9*
          b{1,#,0}(2) -> 1*
          12 -> 4*
          11 -> 10*
          6 -> 1*
          13 -> 7*
          8 -> 5*
          1 -> 8*
          5 -> 1*
          9 -> 5*
          3 -> 8*
        problem:
         DPs:
          
         TRS:
          a1(a1(x)) -> c1(b1(x))
          b1(b1(x)) -> a1(c1(x))
          c1(c1(x)) -> b1(a1(x))
        Qed