YES

Problem:
 b(c(a(x1))) -> a(b(x1))
 b(b(b(x1))) -> c(a(c(x1)))
 c(d(x1)) -> d(c(x1))
 c(d(b(x1))) -> d(c(c(x1)))
 d(c(x1)) -> b(b(b(x1)))
 c(b(x1)) -> d(a(x1))
 d(b(c(x1))) -> a(a(x1))
 d(a(x1)) -> b(x1)

Proof:
 DP Processor:
  DPs:
   b#(c(a(x1))) -> b#(x1)
   b#(b(b(x1))) -> c#(x1)
   b#(b(b(x1))) -> c#(a(c(x1)))
   c#(d(x1)) -> c#(x1)
   c#(d(x1)) -> d#(c(x1))
   c#(d(b(x1))) -> c#(x1)
   c#(d(b(x1))) -> c#(c(x1))
   c#(d(b(x1))) -> d#(c(c(x1)))
   d#(c(x1)) -> b#(x1)
   d#(c(x1)) -> b#(b(x1))
   d#(c(x1)) -> b#(b(b(x1)))
   c#(b(x1)) -> d#(a(x1))
   d#(a(x1)) -> b#(x1)
  TRS:
   b(c(a(x1))) -> a(b(x1))
   b(b(b(x1))) -> c(a(c(x1)))
   c(d(x1)) -> d(c(x1))
   c(d(b(x1))) -> d(c(c(x1)))
   d(c(x1)) -> b(b(b(x1)))
   c(b(x1)) -> d(a(x1))
   d(b(c(x1))) -> a(a(x1))
   d(a(x1)) -> b(x1)
  TDG Processor:
   DPs:
    b#(c(a(x1))) -> b#(x1)
    b#(b(b(x1))) -> c#(x1)
    b#(b(b(x1))) -> c#(a(c(x1)))
    c#(d(x1)) -> c#(x1)
    c#(d(x1)) -> d#(c(x1))
    c#(d(b(x1))) -> c#(x1)
    c#(d(b(x1))) -> c#(c(x1))
    c#(d(b(x1))) -> d#(c(c(x1)))
    d#(c(x1)) -> b#(x1)
    d#(c(x1)) -> b#(b(x1))
    d#(c(x1)) -> b#(b(b(x1)))
    c#(b(x1)) -> d#(a(x1))
    d#(a(x1)) -> b#(x1)
   TRS:
    b(c(a(x1))) -> a(b(x1))
    b(b(b(x1))) -> c(a(c(x1)))
    c(d(x1)) -> d(c(x1))
    c(d(b(x1))) -> d(c(c(x1)))
    d(c(x1)) -> b(b(b(x1)))
    c(b(x1)) -> d(a(x1))
    d(b(c(x1))) -> a(a(x1))
    d(a(x1)) -> b(x1)
   graph:
    d#(c(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> c#(a(c(x1)))
    d#(c(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> c#(x1)
    d#(c(x1)) -> b#(b(b(x1))) -> b#(c(a(x1))) -> b#(x1)
    d#(c(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(a(c(x1)))
    d#(c(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(x1)
    d#(c(x1)) -> b#(b(x1)) -> b#(c(a(x1))) -> b#(x1)
    d#(c(x1)) -> b#(x1) -> b#(b(b(x1))) -> c#(a(c(x1)))
    d#(c(x1)) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
    d#(c(x1)) -> b#(x1) -> b#(c(a(x1))) -> b#(x1)
    d#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> c#(a(c(x1)))
    d#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
    d#(a(x1)) -> b#(x1) -> b#(c(a(x1))) -> b#(x1)
    c#(d(b(x1))) -> d#(c(c(x1))) -> d#(a(x1)) -> b#(x1)
    c#(d(b(x1))) -> d#(c(c(x1))) -> d#(c(x1)) -> b#(b(b(x1)))
    c#(d(b(x1))) -> d#(c(c(x1))) -> d#(c(x1)) -> b#(b(x1))
    c#(d(b(x1))) -> d#(c(c(x1))) -> d#(c(x1)) -> b#(x1)
    c#(d(b(x1))) -> c#(c(x1)) -> c#(b(x1)) -> d#(a(x1))
    c#(d(b(x1))) -> c#(c(x1)) -> c#(d(b(x1))) -> d#(c(c(x1)))
    c#(d(b(x1))) -> c#(c(x1)) -> c#(d(b(x1))) -> c#(c(x1))
    c#(d(b(x1))) -> c#(c(x1)) -> c#(d(b(x1))) -> c#(x1)
    c#(d(b(x1))) -> c#(c(x1)) -> c#(d(x1)) -> d#(c(x1))
    c#(d(b(x1))) -> c#(c(x1)) -> c#(d(x1)) -> c#(x1)
    c#(d(b(x1))) -> c#(x1) -> c#(b(x1)) -> d#(a(x1))
    c#(d(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> d#(c(c(x1)))
    c#(d(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> c#(c(x1))
    c#(d(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> c#(x1)
    c#(d(b(x1))) -> c#(x1) -> c#(d(x1)) -> d#(c(x1))
    c#(d(b(x1))) -> c#(x1) -> c#(d(x1)) -> c#(x1)
    c#(d(x1)) -> d#(c(x1)) -> d#(a(x1)) -> b#(x1)
    c#(d(x1)) -> d#(c(x1)) -> d#(c(x1)) -> b#(b(b(x1)))
    c#(d(x1)) -> d#(c(x1)) -> d#(c(x1)) -> b#(b(x1))
    c#(d(x1)) -> d#(c(x1)) -> d#(c(x1)) -> b#(x1)
    c#(d(x1)) -> c#(x1) -> c#(b(x1)) -> d#(a(x1))
    c#(d(x1)) -> c#(x1) -> c#(d(b(x1))) -> d#(c(c(x1)))
    c#(d(x1)) -> c#(x1) -> c#(d(b(x1))) -> c#(c(x1))
    c#(d(x1)) -> c#(x1) -> c#(d(b(x1))) -> c#(x1)
    c#(d(x1)) -> c#(x1) -> c#(d(x1)) -> d#(c(x1))
    c#(d(x1)) -> c#(x1) -> c#(d(x1)) -> c#(x1)
    c#(b(x1)) -> d#(a(x1)) -> d#(a(x1)) -> b#(x1)
    c#(b(x1)) -> d#(a(x1)) -> d#(c(x1)) -> b#(b(b(x1)))
    c#(b(x1)) -> d#(a(x1)) -> d#(c(x1)) -> b#(b(x1))
    c#(b(x1)) -> d#(a(x1)) -> d#(c(x1)) -> b#(x1)
    b#(b(b(x1))) -> c#(a(c(x1))) -> c#(b(x1)) -> d#(a(x1))
    b#(b(b(x1))) -> c#(a(c(x1))) -> c#(d(b(x1))) -> d#(c(c(x1)))
    b#(b(b(x1))) -> c#(a(c(x1))) -> c#(d(b(x1))) -> c#(c(x1))
    b#(b(b(x1))) -> c#(a(c(x1))) -> c#(d(b(x1))) -> c#(x1)
    b#(b(b(x1))) -> c#(a(c(x1))) -> c#(d(x1)) -> d#(c(x1))
    b#(b(b(x1))) -> c#(a(c(x1))) -> c#(d(x1)) -> c#(x1)
    b#(b(b(x1))) -> c#(x1) -> c#(b(x1)) -> d#(a(x1))
    b#(b(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> d#(c(c(x1)))
    b#(b(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> c#(c(x1))
    b#(b(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> c#(x1)
    b#(b(b(x1))) -> c#(x1) -> c#(d(x1)) -> d#(c(x1))
    b#(b(b(x1))) -> c#(x1) -> c#(d(x1)) -> c#(x1)
    b#(c(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(a(c(x1)))
    b#(c(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
    b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> b#(x1)
   EDG Processor:
    DPs:
     b#(c(a(x1))) -> b#(x1)
     b#(b(b(x1))) -> c#(x1)
     b#(b(b(x1))) -> c#(a(c(x1)))
     c#(d(x1)) -> c#(x1)
     c#(d(x1)) -> d#(c(x1))
     c#(d(b(x1))) -> c#(x1)
     c#(d(b(x1))) -> c#(c(x1))
     c#(d(b(x1))) -> d#(c(c(x1)))
     d#(c(x1)) -> b#(x1)
     d#(c(x1)) -> b#(b(x1))
     d#(c(x1)) -> b#(b(b(x1)))
     c#(b(x1)) -> d#(a(x1))
     d#(a(x1)) -> b#(x1)
    TRS:
     b(c(a(x1))) -> a(b(x1))
     b(b(b(x1))) -> c(a(c(x1)))
     c(d(x1)) -> d(c(x1))
     c(d(b(x1))) -> d(c(c(x1)))
     d(c(x1)) -> b(b(b(x1)))
     c(b(x1)) -> d(a(x1))
     d(b(c(x1))) -> a(a(x1))
     d(a(x1)) -> b(x1)
    graph:
     d#(c(x1)) -> b#(b(b(x1))) -> b#(c(a(x1))) -> b#(x1)
     d#(c(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> c#(x1)
     d#(c(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> c#(a(c(x1)))
     d#(c(x1)) -> b#(b(x1)) -> b#(c(a(x1))) -> b#(x1)
     d#(c(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(x1)
     d#(c(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(a(c(x1)))
     d#(c(x1)) -> b#(x1) -> b#(c(a(x1))) -> b#(x1)
     d#(c(x1)) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
     d#(c(x1)) -> b#(x1) -> b#(b(b(x1))) -> c#(a(c(x1)))
     d#(a(x1)) -> b#(x1) -> b#(c(a(x1))) -> b#(x1)
     d#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
     d#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> c#(a(c(x1)))
     c#(d(b(x1))) -> d#(c(c(x1))) -> d#(c(x1)) -> b#(x1)
     c#(d(b(x1))) -> d#(c(c(x1))) -> d#(c(x1)) -> b#(b(x1))
     c#(d(b(x1))) -> d#(c(c(x1))) -> d#(c(x1)) -> b#(b(b(x1)))
     c#(d(b(x1))) -> d#(c(c(x1))) -> d#(a(x1)) -> b#(x1)
     c#(d(b(x1))) -> c#(c(x1)) -> c#(d(x1)) -> c#(x1)
     c#(d(b(x1))) -> c#(c(x1)) -> c#(d(x1)) -> d#(c(x1))
     c#(d(b(x1))) -> c#(c(x1)) -> c#(d(b(x1))) -> c#(x1)
     c#(d(b(x1))) -> c#(c(x1)) -> c#(d(b(x1))) -> c#(c(x1))
     c#(d(b(x1))) -> c#(c(x1)) -> c#(d(b(x1))) -> d#(c(c(x1)))
     c#(d(b(x1))) -> c#(c(x1)) -> c#(b(x1)) -> d#(a(x1))
     c#(d(b(x1))) -> c#(x1) -> c#(d(x1)) -> c#(x1)
     c#(d(b(x1))) -> c#(x1) -> c#(d(x1)) -> d#(c(x1))
     c#(d(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> c#(x1)
     c#(d(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> c#(c(x1))
     c#(d(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> d#(c(c(x1)))
     c#(d(b(x1))) -> c#(x1) -> c#(b(x1)) -> d#(a(x1))
     c#(d(x1)) -> d#(c(x1)) -> d#(c(x1)) -> b#(x1)
     c#(d(x1)) -> d#(c(x1)) -> d#(c(x1)) -> b#(b(x1))
     c#(d(x1)) -> d#(c(x1)) -> d#(c(x1)) -> b#(b(b(x1)))
     c#(d(x1)) -> d#(c(x1)) -> d#(a(x1)) -> b#(x1)
     c#(d(x1)) -> c#(x1) -> c#(d(x1)) -> c#(x1)
     c#(d(x1)) -> c#(x1) -> c#(d(x1)) -> d#(c(x1))
     c#(d(x1)) -> c#(x1) -> c#(d(b(x1))) -> c#(x1)
     c#(d(x1)) -> c#(x1) -> c#(d(b(x1))) -> c#(c(x1))
     c#(d(x1)) -> c#(x1) -> c#(d(b(x1))) -> d#(c(c(x1)))
     c#(d(x1)) -> c#(x1) -> c#(b(x1)) -> d#(a(x1))
     c#(b(x1)) -> d#(a(x1)) -> d#(a(x1)) -> b#(x1)
     b#(b(b(x1))) -> c#(x1) -> c#(d(x1)) -> c#(x1)
     b#(b(b(x1))) -> c#(x1) -> c#(d(x1)) -> d#(c(x1))
     b#(b(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> c#(x1)
     b#(b(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> c#(c(x1))
     b#(b(b(x1))) -> c#(x1) -> c#(d(b(x1))) -> d#(c(c(x1)))
     b#(b(b(x1))) -> c#(x1) -> c#(b(x1)) -> d#(a(x1))
     b#(c(a(x1))) -> b#(x1) -> b#(c(a(x1))) -> b#(x1)
     b#(c(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
     b#(c(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(a(c(x1)))
    SCC Processor:
     #sccs: 1
     #rules: 12
     #arcs: 48/169
     DPs:
      d#(c(x1)) -> b#(b(b(x1)))
      b#(b(b(x1))) -> c#(x1)
      c#(b(x1)) -> d#(a(x1))
      d#(a(x1)) -> b#(x1)
      b#(c(a(x1))) -> b#(x1)
      c#(d(b(x1))) -> d#(c(c(x1)))
      d#(c(x1)) -> b#(b(x1))
      d#(c(x1)) -> b#(x1)
      c#(d(b(x1))) -> c#(c(x1))
      c#(d(b(x1))) -> c#(x1)
      c#(d(x1)) -> d#(c(x1))
      c#(d(x1)) -> c#(x1)
     TRS:
      b(c(a(x1))) -> a(b(x1))
      b(b(b(x1))) -> c(a(c(x1)))
      c(d(x1)) -> d(c(x1))
      c(d(b(x1))) -> d(c(c(x1)))
      d(c(x1)) -> b(b(b(x1)))
      c(b(x1)) -> d(a(x1))
      d(b(c(x1))) -> a(a(x1))
      d(a(x1)) -> b(x1)
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [d#](x0) = 9x0,
       
       [c#](x0) = 8x0,
       
       [b#](x0) = 7x0,
       
       [d](x0) = 2x0,
       
       [b](x0) = 1x0,
       
       [c](x0) = 1x0,
       
       [a](x0) = x0
      orientation:
       d#(c(x1)) = 10x1 >= 9x1 = b#(b(b(x1)))
       
       b#(b(b(x1))) = 9x1 >= 8x1 = c#(x1)
       
       c#(b(x1)) = 9x1 >= 9x1 = d#(a(x1))
       
       d#(a(x1)) = 9x1 >= 7x1 = b#(x1)
       
       b#(c(a(x1))) = 8x1 >= 7x1 = b#(x1)
       
       c#(d(b(x1))) = 11x1 >= 11x1 = d#(c(c(x1)))
       
       d#(c(x1)) = 10x1 >= 8x1 = b#(b(x1))
       
       d#(c(x1)) = 10x1 >= 7x1 = b#(x1)
       
       c#(d(b(x1))) = 11x1 >= 9x1 = c#(c(x1))
       
       c#(d(b(x1))) = 11x1 >= 8x1 = c#(x1)
       
       c#(d(x1)) = 10x1 >= 10x1 = d#(c(x1))
       
       c#(d(x1)) = 10x1 >= 8x1 = c#(x1)
       
       b(c(a(x1))) = 2x1 >= 1x1 = a(b(x1))
       
       b(b(b(x1))) = 3x1 >= 2x1 = c(a(c(x1)))
       
       c(d(x1)) = 3x1 >= 3x1 = d(c(x1))
       
       c(d(b(x1))) = 4x1 >= 4x1 = d(c(c(x1)))
       
       d(c(x1)) = 3x1 >= 3x1 = b(b(b(x1)))
       
       c(b(x1)) = 2x1 >= 2x1 = d(a(x1))
       
       d(b(c(x1))) = 4x1 >= x1 = a(a(x1))
       
       d(a(x1)) = 2x1 >= 1x1 = b(x1)
      problem:
       DPs:
        c#(b(x1)) -> d#(a(x1))
        c#(d(b(x1))) -> d#(c(c(x1)))
        c#(d(x1)) -> d#(c(x1))
       TRS:
        b(c(a(x1))) -> a(b(x1))
        b(b(b(x1))) -> c(a(c(x1)))
        c(d(x1)) -> d(c(x1))
        c(d(b(x1))) -> d(c(c(x1)))
        d(c(x1)) -> b(b(b(x1)))
        c(b(x1)) -> d(a(x1))
        d(b(c(x1))) -> a(a(x1))
        d(a(x1)) -> b(x1)
      EDG Processor:
       DPs:
        c#(b(x1)) -> d#(a(x1))
        c#(d(b(x1))) -> d#(c(c(x1)))
        c#(d(x1)) -> d#(c(x1))
       TRS:
        b(c(a(x1))) -> a(b(x1))
        b(b(b(x1))) -> c(a(c(x1)))
        c(d(x1)) -> d(c(x1))
        c(d(b(x1))) -> d(c(c(x1)))
        d(c(x1)) -> b(b(b(x1)))
        c(b(x1)) -> d(a(x1))
        d(b(c(x1))) -> a(a(x1))
        d(a(x1)) -> b(x1)
       graph:
        
       Qed