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))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0) = x0 + 0,
        
        [f](x0) = 1x0 + 1,
        
        [b](x0, x1) = x0 + 1x1 + 0,
        
        [c](x0, x1, x2) = 1x0 + 1x1 + x2 + 2,
        
        [a] = 0
       orientation:
        f#(b(b(x,f(y)),z)) = x + 2y + 1z + 2 >= 1y + 1 = f#(b(b(f(a()),y),y))
        
        f(c(c(a(),y,a()),b(x,z),a())) = 2x + 3y + 3z + 4 >= y + 3z + 4 = b(y,f(c(f(a()),z,z)))
        
        f(b(b(x,f(y)),z)) = 1x + 3y + 2z + 3 >= 1x + 2y + 1z + 2 = c(z,x,f(b(b(f(a()),y),y)))
        
        c(b(a(),a()),b(y,z),x) = x + 1y + 2z + 2 >= 2z + 1 = b(a(),b(z,z))
       problem:
        DPs:
         
        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))
       Qed