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

Proof:
 DP Processor:
  DPs:
   f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a())
   f#(c(c(a(),y,a()),b(x,z),a())) -> c#(f(a()),z,z)
   f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z))
   f#(b(b(x,f(y)),z)) -> f#(a())
   f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
   f#(b(b(x,f(y)),z)) -> c#(z,x,f(b(b(f(a()),y),y)))
  TRS:
   f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
   f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
   c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
  TDG Processor:
   DPs:
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a())
    f#(c(c(a(),y,a()),b(x,z),a())) -> c#(f(a()),z,z)
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z))
    f#(b(b(x,f(y)),z)) -> f#(a())
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
    f#(b(b(x,f(y)),z)) -> c#(z,x,f(b(b(f(a()),y),y)))
   TRS:
    f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
    f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
    c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
   graph:
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y)) ->
    f#(b(b(x,f(y)),z)) -> c#(z,x,f(b(b(f(a()),y),y)))
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y)) ->
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y)) ->
    f#(b(b(x,f(y)),z)) -> f#(a())
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y)) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z))
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y)) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> c#(f(a()),z,z)
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y)) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a())
    f#(b(b(x,f(y)),z)) -> f#(a()) ->
    f#(b(b(x,f(y)),z)) -> c#(z,x,f(b(b(f(a()),y),y)))
    f#(b(b(x,f(y)),z)) -> f#(a()) ->
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
    f#(b(b(x,f(y)),z)) -> f#(a()) -> f#(b(b(x,f(y)),z)) -> f#(a())
    f#(b(b(x,f(y)),z)) -> f#(a()) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z))
    f#(b(b(x,f(y)),z)) -> f#(a()) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> c#(f(a()),z,z)
    f#(b(b(x,f(y)),z)) -> f#(a()) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a())
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z)) ->
    f#(b(b(x,f(y)),z)) -> c#(z,x,f(b(b(f(a()),y),y)))
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z)) ->
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z)) ->
    f#(b(b(x,f(y)),z)) -> f#(a())
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z)) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z))
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z)) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> c#(f(a()),z,z)
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z)) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a())
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a()) ->
    f#(b(b(x,f(y)),z)) -> c#(z,x,f(b(b(f(a()),y),y)))
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a()) ->
    f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a()) ->
    f#(b(b(x,f(y)),z)) -> f#(a())
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a()) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z))
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a()) ->
    f#(c(c(a(),y,a()),b(x,z),a())) -> c#(f(a()),z,z)
    f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a()) -> f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a())
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 24/36
    DPs:
     f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
     f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a())
     f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z))
     f#(b(b(x,f(y)),z)) -> f#(a())
    TRS:
     f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
     f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
     c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
    EDG Processor:
     DPs:
      f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
      f#(c(c(a(),y,a()),b(x,z),a())) -> f#(a())
      f#(c(c(a(),y,a()),b(x,z),a())) -> f#(c(f(a()),z,z))
      f#(b(b(x,f(y)),z)) -> f#(a())
     TRS:
      f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
      f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
      c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
     graph:
      f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y)) ->
      f#(b(b(x,f(y)),z)) -> f#(a())
      f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y)) -> f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 2/16
      DPs:
       f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
      TRS:
       f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
       f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
       c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
      Usable Rule Processor:
       DPs:
        f#(b(b(x,f(y)),z)) -> f#(b(b(f(a()),y),y))
       TRS:
        
       Arctic Interpretation Processor:
        dimension: 1
        usable rules:
         
        interpretation:
         [f#](x0) = x0 + 0,
         
         [f](x0) = 5x0 + 5,
         
         [b](x0, x1) = -4x0 + 1x1,
         
         [a] = 0
        orientation:
         f#(b(b(x,f(y)),z)) = -8x + 2y + 1z + 2 >= 1y + 0 = f#(b(b(f(a()),y),y))
        problem:
         DPs:
          
         TRS:
          
        Qed