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

Proof:
 DP Processor:
  DPs:
   c#(c(z,x,a()),a(),y) -> c#(z,y,x)
   c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
   c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
   c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
   c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
   f#(f(c(a(),y,z))) -> b#(z,z)
   f#(f(c(a(),y,z))) -> b#(y,b(z,z))
  TRS:
   b(a(),f(b(b(z,y),a()))) -> z
   c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
   f(f(c(a(),y,z))) -> b(y,b(z,z))
  TDG Processor:
   DPs:
    c#(c(z,x,a()),a(),y) -> c#(z,y,x)
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
    f#(f(c(a(),y,z))) -> b#(z,z)
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
   TRS:
    b(a(),f(b(b(z,y),a()))) -> z
    c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
    f(f(c(a(),y,z))) -> b(y,b(z,z))
   graph:
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x)))) ->
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x)))) ->
    f#(f(c(a(),y,z))) -> b#(z,z)
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x)) ->
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x)) ->
    f#(f(c(a(),y,z))) -> b#(z,z)
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x))))) ->
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x))))) ->
    f#(f(c(a(),y,z))) -> b#(z,z)
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> c#(z,y,x)
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) -> c#(c(z,x,a()),a(),y) -> c#(z,y,x)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 16/49
    DPs:
     c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
     c#(c(z,x,a()),a(),y) -> c#(z,y,x)
    TRS:
     b(a(),f(b(b(z,y),a()))) -> z
     c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
     f(f(c(a(),y,z))) -> b(y,b(z,z))
    Matrix Interpretation Processor: dim=3
     
     usable rules:
      b(a(),f(b(b(z,y),a()))) -> z
      c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
      f(f(c(a(),y,z))) -> b(y,b(z,z))
     interpretation:
                    [1 1 1]     [0 0 1]  
      [b](x0, x1) = [0 0 0]x0 + [0 1 0]x1
                    [1 0 0]     [0 1 0]  ,
      
                        [1 1 1]     [1 0 0]     [0 0 0]     [1]
      [c](x0, x1, x2) = [0 0 0]x0 + [1 1 1]x1 + [1 1 0]x2 + [0]
                        [0 0 0]     [0 0 0]     [0 0 0]     [0],
      
      [c#](x0, x1, x2) = [1 0 0]x0 + [1 0 0]x2 + [1],
      
            [0]
      [a] = [0]
            [0],
      
                [0 0 1]  
      [f](x0) = [0 0 1]x0
                [0 1 1]  
     orientation:
      c#(c(z,x,a()),a(),y) = [1 0 0]x + [1 0 0]y + [1 1 1]z + [2] >= [1 0 0]y + [1] = c#(y,a(),f(c(z,y,x)))
      
      c#(c(z,x,a()),a(),y) = [1 0 0]x + [1 0 0]y + [1 1 1]z + [2] >= [1 0 0]x + [1 0 0]z + [1] = c#(z,y,x)
      
                                [0 0 1]    [1 1 1]          
      b(a(),f(b(b(z,y),a()))) = [0 0 1]y + [1 1 1]z >= z = z
                                [0 0 1]    [1 1 1]          
      
                            [2 1 1]    [0 0 0]    [1 1 1]    [2]    [0]                             
      c(c(z,x,a()),a(),y) = [0 0 0]x + [1 1 0]y + [0 0 0]z + [0] >= [0] = f(f(c(y,a(),f(c(z,y,x)))))
                            [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0]                             
      
                         [1 1 1]    [1 1 0]     [1 1 1]    [1 1 0]               
      f(f(c(a(),y,z))) = [1 1 1]y + [1 1 0]z >= [0 0 0]y + [0 1 0]z = b(y,b(z,z))
                         [1 1 1]    [1 1 0]     [1 0 0]    [0 1 0]               
     problem:
      DPs:
       
      TRS:
       b(a(),f(b(b(z,y),a()))) -> z
       c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
       f(f(c(a(),y,z))) -> b(y,b(z,z))
     Qed