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


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YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
   b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
   b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
   f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x)
   f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y)
   f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y))
   c#(f(c(a(),y,a())),x,z) -> b#(x,a())
   c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
   c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a())))
   c#(f(c(a(),y,a())),x,z) -> b#(z,z)
   c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a()))))
   c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a())))))
  TRS:
   b(a(),b(c(z,x,y),a())) -> b(b(z,c(y,z,a())),x)
   f(c(a(),b(b(z,a()),y),x)) -> f(c(x,b(z,x),y))
   c(f(c(a(),y,a())),x,z) -> f(b(b(z,z),f(b(y,b(x,a())))))
  TDG Processor:
   DPs:
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
    f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x)
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y)
    f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y))
    c#(f(c(a(),y,a())),x,z) -> b#(x,a())
    c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
    c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a())))
    c#(f(c(a(),y,a())),x,z) -> b#(z,z)
    c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a()))))
    c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a())))))
   TRS:
    b(a(),b(c(z,x,y),a())) -> b(b(z,c(y,z,a())),x)
    f(c(a(),b(b(z,a()),y),x)) -> f(c(x,b(z,x),y))
    c(f(c(a(),y,a())),x,z) -> f(b(b(z,z),f(b(y,b(x,a())))))
   graph:
    f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y)) ->
    f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y))
    f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y)) ->
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y)
    f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y)) ->
    f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x)
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
    c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a())))))
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
    c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a()))))
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
    c#(f(c(a(),y,a())),x,z) -> b#(z,z)
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
    c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a())))
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
    c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
    c#(f(c(a(),y,a())),x,z) -> b#(x,a())
    f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x) ->
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
    f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x) ->
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
    f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x) ->
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
    c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a()))))) ->
    f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y))
    c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a()))))) ->
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y)
    c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a()))))) ->
    f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x)
    c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a()))) ->
    f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y))
    c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a()))) ->
    f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y)
    c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a()))) ->
    f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x)
    c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a())))) ->
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
    c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a())))) ->
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
    c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a())))) ->
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
    c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a())) ->
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
    c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a())) ->
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
    c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a())) ->
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
    c#(f(c(a(),y,a())),x,z) -> b#(x,a()) ->
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
    c#(f(c(a(),y,a())),x,z) -> b#(x,a()) ->
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
    c#(f(c(a(),y,a())),x,z) -> b#(x,a()) ->
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
    c#(f(c(a(),y,a())),x,z) -> b#(z,z) ->
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
    c#(f(c(a(),y,a())),x,z) -> b#(z,z) ->
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
    c#(f(c(a(),y,a())),x,z) -> b#(z,z) ->
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
    c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a())))))
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
    c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a()))))
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
    c#(f(c(a(),y,a())),x,z) -> b#(z,z)
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
    c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a())))
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
    c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
    c#(f(c(a(),y,a())),x,z) -> b#(x,a())
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x) ->
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x) ->
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x) ->
    b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a())) ->
    b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a())) ->
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
    b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a())) -> b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
   EDG Processor:
    DPs:
     b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
     b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
     b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
     f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x)
     f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y)
     f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y))
     c#(f(c(a(),y,a())),x,z) -> b#(x,a())
     c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
     c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a())))
     c#(f(c(a(),y,a())),x,z) -> b#(z,z)
     c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a()))))
     c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a())))))
    TRS:
     b(a(),b(c(z,x,y),a())) -> b(b(z,c(y,z,a())),x)
     f(c(a(),b(b(z,a()),y),x)) -> f(c(x,b(z,x),y))
     c(f(c(a(),y,a())),x,z) -> f(b(b(z,z),f(b(y,b(x,a())))))
    graph:
     f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y)) ->
     f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x)
     f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y)) ->
     f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y)
     f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y)) ->
     f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y))
     f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
     c#(f(c(a(),y,a())),x,z) -> b#(x,a())
     f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
     c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
     f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
     c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a())))
     f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
     c#(f(c(a(),y,a())),x,z) -> b#(z,z)
     f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
     c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a()))))
     f#(c(a(),b(b(z,a()),y),x)) -> c#(x,b(z,x),y) ->
     c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a())))))
     f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x) ->
     b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
     f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x) ->
     b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
     f#(c(a(),b(b(z,a()),y),x)) -> b#(z,x) ->
     b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
     c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a())) ->
     b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
     c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a())) ->
     b#(a(),b(c(z,x,y),a())) -> b#(z,c(y,z,a()))
     c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a())) ->
     b#(a(),b(c(z,x,y),a())) -> b#(b(z,c(y,z,a())),x)
     b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
     c#(f(c(a(),y,a())),x,z) -> b#(x,a())
     b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
     c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
     b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
     c#(f(c(a(),y,a())),x,z) -> f#(b(y,b(x,a())))
     b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
     c#(f(c(a(),y,a())),x,z) -> b#(z,z)
     b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
     c#(f(c(a(),y,a())),x,z) -> b#(b(z,z),f(b(y,b(x,a()))))
     b#(a(),b(c(z,x,y),a())) -> c#(y,z,a()) ->
     c#(f(c(a(),y,a())),x,z) -> f#(b(b(z,z),f(b(y,b(x,a())))))
    SCC Processor:
     #sccs: 2
     #rules: 3
     #arcs: 21/144
     DPs:
      f#(c(a(),b(b(z,a()),y),x)) -> f#(c(x,b(z,x),y))
     TRS:
      b(a(),b(c(z,x,y),a())) -> b(b(z,c(y,z,a())),x)
      f(c(a(),b(b(z,a()),y),x)) -> f(c(x,b(z,x),y))
      c(f(c(a(),y,a())),x,z) -> f(b(b(z,z),f(b(y,b(x,a())))))
     Matrix Interpretation Processor: dim=2
      
      usable rules:
       b(a(),b(c(z,x,y),a())) -> b(b(z,c(y,z,a())),x)
       f(c(a(),b(b(z,a()),y),x)) -> f(c(x,b(z,x),y))
       c(f(c(a(),y,a())),x,z) -> f(b(b(z,z),f(b(y,b(x,a())))))
      interpretation:
                         [2 1]     [0 0]     [2 2]     [0]
       [c](x0, x1, x2) = [0 0]x0 + [1 0]x1 + [1 0]x2 + [2],
       
                 [0 0]     [1]
       [f](x0) = [0 1]x0 + [0],
       
             [0]
       [a] = [0],
       
       [f#](x0) = [0 1]x0,
       
                     [2 1]     [1 0]     [0]
       [b](x0, x1) = [0 0]x0 + [0 0]x1 + [1]
      orientation:
       f#(c(a(),b(b(z,a()),y),x)) = [1 0]x + [1 0]y + [4 2]z + [3] >= [1 0]x + [1 0]y + [2 1]z + [2] = f#(c(x,b(z,x),y))
       
                                [1 0]    [5 4]    [4 2]    [2]    [1 0]    [4 2]    [4 2]    [1]                       
       b(a(),b(c(z,x,y),a())) = [0 0]x + [0 0]y + [0 0]z + [1] >= [0 0]x + [0 0]y + [0 0]z + [1] = b(b(z,c(y,z,a())),x)
       
                                   [0 0]    [0 0]    [0 0]    [1]    [0 0]    [0 0]    [0 0]    [1]                   
       f(c(a(),b(b(z,a()),y),x)) = [1 0]x + [1 0]y + [4 2]z + [3] >= [1 0]x + [1 0]y + [2 1]z + [2] = f(c(x,b(z,x),y))
       
                                [0 0]    [1 0]    [2 2]    [4]    [1]                                
       c(f(c(a(),y,a())),x,z) = [1 0]x + [0 0]y + [1 0]z + [2] >= [1] = f(b(b(z,z),f(b(y,b(x,a())))))
      problem:
       DPs:
        
       TRS:
        b(a(),b(c(z,x,y),a())) -> b(b(z,c(y,z,a())),x)
        f(c(a(),b(b(z,a()),y),x)) -> f(c(x,b(z,x),y))
        c(f(c(a(),y,a())),x,z) -> f(b(b(z,z),f(b(y,b(x,a())))))
      Qed
     
     DPs:
      c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
      b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
     TRS:
      b(a(),b(c(z,x,y),a())) -> b(b(z,c(y,z,a())),x)
      f(c(a(),b(b(z,a()),y),x)) -> f(c(x,b(z,x),y))
      c(f(c(a(),y,a())),x,z) -> f(b(b(z,z),f(b(y,b(x,a())))))
     Usable Rule Processor:
      DPs:
       c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
       b#(a(),b(c(z,x,y),a())) -> c#(y,z,a())
      TRS:
       
      Semantic Labeling Processor:
       dimension: 1
       usable rules:
        
       interpretation:
        [c](x0, x1, x2) = 0,
        
        [f](x0) = 0,
        
        [a] = 1,
        
        [b](x0, x1) = 0
        labeled:
        usable (for model):
        argument filtering:
         pi(a) = []
         pi(c) = [0]
         pi(b) = 0
         pi(f) = 0
         pi(b#) = 1
         pi(c#) = 1
       precedence:
        c# ~ b# ~ f ~ b ~ c ~ a
       problem:
        DPs:
         c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
        TRS:
         
       Restore Modifier:
        DPs:
         c#(f(c(a(),y,a())),x,z) -> b#(y,b(x,a()))
        TRS:
         b(a(),b(c(z,x,y),a())) -> b(b(z,c(y,z,a())),x)
         f(c(a(),b(b(z,a()),y),x)) -> f(c(x,b(z,x),y))
         c(f(c(a(),y,a())),x,z) -> f(b(b(z,z),f(b(y,b(x,a())))))
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 2/1