YES

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

Proof:
 DP Processor:
  DPs:
   b#(b(x1)) -> d#(x1)
   b#(b(x1)) -> c#(d(x1))
   c#(c(x1)) -> d#(x1)
   c#(c(x1)) -> d#(d(x1))
   c#(c(x1)) -> d#(d(d(x1)))
   c#(x1) -> g#(x1)
   d#(d(x1)) -> f#(x1)
   d#(d(x1)) -> c#(f(x1))
   d#(d(d(x1))) -> c#(x1)
   d#(d(d(x1))) -> g#(c(x1))
   f#(x1) -> g#(x1)
   g#(x1) -> b#(x1)
   g#(x1) -> d#(a(b(x1)))
   g#(g(x1)) -> c#(x1)
   g#(g(x1)) -> b#(c(x1))
  TRS:
   b(b(x1)) -> c(d(x1))
   c(c(x1)) -> d(d(d(x1)))
   c(x1) -> g(x1)
   d(d(x1)) -> c(f(x1))
   d(d(d(x1))) -> g(c(x1))
   f(x1) -> a(g(x1))
   g(x1) -> d(a(b(x1)))
   g(g(x1)) -> b(c(x1))
  TDG Processor:
   DPs:
    b#(b(x1)) -> d#(x1)
    b#(b(x1)) -> c#(d(x1))
    c#(c(x1)) -> d#(x1)
    c#(c(x1)) -> d#(d(x1))
    c#(c(x1)) -> d#(d(d(x1)))
    c#(x1) -> g#(x1)
    d#(d(x1)) -> f#(x1)
    d#(d(x1)) -> c#(f(x1))
    d#(d(d(x1))) -> c#(x1)
    d#(d(d(x1))) -> g#(c(x1))
    f#(x1) -> g#(x1)
    g#(x1) -> b#(x1)
    g#(x1) -> d#(a(b(x1)))
    g#(g(x1)) -> c#(x1)
    g#(g(x1)) -> b#(c(x1))
   TRS:
    b(b(x1)) -> c(d(x1))
    c(c(x1)) -> d(d(d(x1)))
    c(x1) -> g(x1)
    d(d(x1)) -> c(f(x1))
    d(d(d(x1))) -> g(c(x1))
    f(x1) -> a(g(x1))
    g(x1) -> d(a(b(x1)))
    g(g(x1)) -> b(c(x1))
   graph:
    f#(x1) -> g#(x1) -> g#(g(x1)) -> b#(c(x1))
    f#(x1) -> g#(x1) -> g#(g(x1)) -> c#(x1)
    f#(x1) -> g#(x1) -> g#(x1) -> d#(a(b(x1)))
    f#(x1) -> g#(x1) -> g#(x1) -> b#(x1)
    g#(g(x1)) -> c#(x1) -> c#(x1) -> g#(x1)
    g#(g(x1)) -> c#(x1) -> c#(c(x1)) -> d#(d(d(x1)))
    g#(g(x1)) -> c#(x1) -> c#(c(x1)) -> d#(d(x1))
    g#(g(x1)) -> c#(x1) -> c#(c(x1)) -> d#(x1)
    g#(g(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(d(x1))
    g#(g(x1)) -> b#(c(x1)) -> b#(b(x1)) -> d#(x1)
    g#(x1) -> d#(a(b(x1))) -> d#(d(d(x1))) -> g#(c(x1))
    g#(x1) -> d#(a(b(x1))) -> d#(d(d(x1))) -> c#(x1)
    g#(x1) -> d#(a(b(x1))) -> d#(d(x1)) -> c#(f(x1))
    g#(x1) -> d#(a(b(x1))) -> d#(d(x1)) -> f#(x1)
    g#(x1) -> b#(x1) -> b#(b(x1)) -> c#(d(x1))
    g#(x1) -> b#(x1) -> b#(b(x1)) -> d#(x1)
    c#(c(x1)) -> d#(d(d(x1))) -> d#(d(d(x1))) -> g#(c(x1))
    c#(c(x1)) -> d#(d(d(x1))) -> d#(d(d(x1))) -> c#(x1)
    c#(c(x1)) -> d#(d(d(x1))) -> d#(d(x1)) -> c#(f(x1))
    c#(c(x1)) -> d#(d(d(x1))) -> d#(d(x1)) -> f#(x1)
    c#(c(x1)) -> d#(d(x1)) -> d#(d(d(x1))) -> g#(c(x1))
    c#(c(x1)) -> d#(d(x1)) -> d#(d(d(x1))) -> c#(x1)
    c#(c(x1)) -> d#(d(x1)) -> d#(d(x1)) -> c#(f(x1))
    c#(c(x1)) -> d#(d(x1)) -> d#(d(x1)) -> f#(x1)
    c#(c(x1)) -> d#(x1) -> d#(d(d(x1))) -> g#(c(x1))
    c#(c(x1)) -> d#(x1) -> d#(d(d(x1))) -> c#(x1)
    c#(c(x1)) -> d#(x1) -> d#(d(x1)) -> c#(f(x1))
    c#(c(x1)) -> d#(x1) -> d#(d(x1)) -> f#(x1)
    c#(x1) -> g#(x1) -> g#(g(x1)) -> b#(c(x1))
    c#(x1) -> g#(x1) -> g#(g(x1)) -> c#(x1)
    c#(x1) -> g#(x1) -> g#(x1) -> d#(a(b(x1)))
    c#(x1) -> g#(x1) -> g#(x1) -> b#(x1)
    d#(d(d(x1))) -> g#(c(x1)) -> g#(g(x1)) -> b#(c(x1))
    d#(d(d(x1))) -> g#(c(x1)) -> g#(g(x1)) -> c#(x1)
    d#(d(d(x1))) -> g#(c(x1)) -> g#(x1) -> d#(a(b(x1)))
    d#(d(d(x1))) -> g#(c(x1)) -> g#(x1) -> b#(x1)
    d#(d(d(x1))) -> c#(x1) -> c#(x1) -> g#(x1)
    d#(d(d(x1))) -> c#(x1) -> c#(c(x1)) -> d#(d(d(x1)))
    d#(d(d(x1))) -> c#(x1) -> c#(c(x1)) -> d#(d(x1))
    d#(d(d(x1))) -> c#(x1) -> c#(c(x1)) -> d#(x1)
    d#(d(x1)) -> f#(x1) -> f#(x1) -> g#(x1)
    d#(d(x1)) -> c#(f(x1)) -> c#(x1) -> g#(x1)
    d#(d(x1)) -> c#(f(x1)) -> c#(c(x1)) -> d#(d(d(x1)))
    d#(d(x1)) -> c#(f(x1)) -> c#(c(x1)) -> d#(d(x1))
    d#(d(x1)) -> c#(f(x1)) -> c#(c(x1)) -> d#(x1)
    b#(b(x1)) -> c#(d(x1)) -> c#(x1) -> g#(x1)
    b#(b(x1)) -> c#(d(x1)) -> c#(c(x1)) -> d#(d(d(x1)))
    b#(b(x1)) -> c#(d(x1)) -> c#(c(x1)) -> d#(d(x1))
    b#(b(x1)) -> c#(d(x1)) -> c#(c(x1)) -> d#(x1)
    b#(b(x1)) -> d#(x1) -> d#(d(d(x1))) -> g#(c(x1))
    b#(b(x1)) -> d#(x1) -> d#(d(d(x1))) -> c#(x1)
    b#(b(x1)) -> d#(x1) -> d#(d(x1)) -> c#(f(x1))
    b#(b(x1)) -> d#(x1) -> d#(d(x1)) -> f#(x1)
   EDG Processor:
    DPs:
     b#(b(x1)) -> d#(x1)
     b#(b(x1)) -> c#(d(x1))
     c#(c(x1)) -> d#(x1)
     c#(c(x1)) -> d#(d(x1))
     c#(c(x1)) -> d#(d(d(x1)))
     c#(x1) -> g#(x1)
     d#(d(x1)) -> f#(x1)
     d#(d(x1)) -> c#(f(x1))
     d#(d(d(x1))) -> c#(x1)
     d#(d(d(x1))) -> g#(c(x1))
     f#(x1) -> g#(x1)
     g#(x1) -> b#(x1)
     g#(x1) -> d#(a(b(x1)))
     g#(g(x1)) -> c#(x1)
     g#(g(x1)) -> b#(c(x1))
    TRS:
     b(b(x1)) -> c(d(x1))
     c(c(x1)) -> d(d(d(x1)))
     c(x1) -> g(x1)
     d(d(x1)) -> c(f(x1))
     d(d(d(x1))) -> g(c(x1))
     f(x1) -> a(g(x1))
     g(x1) -> d(a(b(x1)))
     g(g(x1)) -> b(c(x1))
    graph:
     f#(x1) -> g#(x1) -> g#(x1) -> b#(x1)
     f#(x1) -> g#(x1) -> g#(x1) -> d#(a(b(x1)))
     f#(x1) -> g#(x1) -> g#(g(x1)) -> c#(x1)
     f#(x1) -> g#(x1) -> g#(g(x1)) -> b#(c(x1))
     g#(g(x1)) -> c#(x1) -> c#(c(x1)) -> d#(x1)
     g#(g(x1)) -> c#(x1) -> c#(c(x1)) -> d#(d(x1))
     g#(g(x1)) -> c#(x1) -> c#(c(x1)) -> d#(d(d(x1)))
     g#(g(x1)) -> c#(x1) -> c#(x1) -> g#(x1)
     g#(g(x1)) -> b#(c(x1)) -> b#(b(x1)) -> d#(x1)
     g#(g(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(d(x1))
     g#(x1) -> b#(x1) -> b#(b(x1)) -> d#(x1)
     g#(x1) -> b#(x1) -> b#(b(x1)) -> c#(d(x1))
     c#(c(x1)) -> d#(d(d(x1))) -> d#(d(x1)) -> f#(x1)
     c#(c(x1)) -> d#(d(d(x1))) -> d#(d(x1)) -> c#(f(x1))
     c#(c(x1)) -> d#(d(d(x1))) -> d#(d(d(x1))) -> c#(x1)
     c#(c(x1)) -> d#(d(d(x1))) -> d#(d(d(x1))) -> g#(c(x1))
     c#(c(x1)) -> d#(d(x1)) -> d#(d(x1)) -> f#(x1)
     c#(c(x1)) -> d#(d(x1)) -> d#(d(x1)) -> c#(f(x1))
     c#(c(x1)) -> d#(d(x1)) -> d#(d(d(x1))) -> c#(x1)
     c#(c(x1)) -> d#(d(x1)) -> d#(d(d(x1))) -> g#(c(x1))
     c#(c(x1)) -> d#(x1) -> d#(d(x1)) -> f#(x1)
     c#(c(x1)) -> d#(x1) -> d#(d(x1)) -> c#(f(x1))
     c#(c(x1)) -> d#(x1) -> d#(d(d(x1))) -> c#(x1)
     c#(c(x1)) -> d#(x1) -> d#(d(d(x1))) -> g#(c(x1))
     c#(x1) -> g#(x1) -> g#(x1) -> b#(x1)
     c#(x1) -> g#(x1) -> g#(x1) -> d#(a(b(x1)))
     c#(x1) -> g#(x1) -> g#(g(x1)) -> c#(x1)
     c#(x1) -> g#(x1) -> g#(g(x1)) -> b#(c(x1))
     d#(d(d(x1))) -> g#(c(x1)) -> g#(x1) -> b#(x1)
     d#(d(d(x1))) -> g#(c(x1)) -> g#(x1) -> d#(a(b(x1)))
     d#(d(d(x1))) -> g#(c(x1)) -> g#(g(x1)) -> c#(x1)
     d#(d(d(x1))) -> g#(c(x1)) -> g#(g(x1)) -> b#(c(x1))
     d#(d(d(x1))) -> c#(x1) -> c#(c(x1)) -> d#(x1)
     d#(d(d(x1))) -> c#(x1) -> c#(c(x1)) -> d#(d(x1))
     d#(d(d(x1))) -> c#(x1) -> c#(c(x1)) -> d#(d(d(x1)))
     d#(d(d(x1))) -> c#(x1) -> c#(x1) -> g#(x1)
     d#(d(x1)) -> f#(x1) -> f#(x1) -> g#(x1)
     d#(d(x1)) -> c#(f(x1)) -> c#(c(x1)) -> d#(x1)
     d#(d(x1)) -> c#(f(x1)) -> c#(c(x1)) -> d#(d(x1))
     d#(d(x1)) -> c#(f(x1)) -> c#(c(x1)) -> d#(d(d(x1)))
     d#(d(x1)) -> c#(f(x1)) -> c#(x1) -> g#(x1)
     b#(b(x1)) -> c#(d(x1)) -> c#(c(x1)) -> d#(x1)
     b#(b(x1)) -> c#(d(x1)) -> c#(c(x1)) -> d#(d(x1))
     b#(b(x1)) -> c#(d(x1)) -> c#(c(x1)) -> d#(d(d(x1)))
     b#(b(x1)) -> c#(d(x1)) -> c#(x1) -> g#(x1)
     b#(b(x1)) -> d#(x1) -> d#(d(x1)) -> f#(x1)
     b#(b(x1)) -> d#(x1) -> d#(d(x1)) -> c#(f(x1))
     b#(b(x1)) -> d#(x1) -> d#(d(d(x1))) -> c#(x1)
     b#(b(x1)) -> d#(x1) -> d#(d(d(x1))) -> g#(c(x1))
    SCC Processor:
     #sccs: 1
     #rules: 14
     #arcs: 49/225
     DPs:
      f#(x1) -> g#(x1)
      g#(g(x1)) -> b#(c(x1))
      b#(b(x1)) -> c#(d(x1))
      c#(x1) -> g#(x1)
      g#(g(x1)) -> c#(x1)
      c#(c(x1)) -> d#(d(d(x1)))
      d#(d(d(x1))) -> g#(c(x1))
      g#(x1) -> b#(x1)
      b#(b(x1)) -> d#(x1)
      d#(d(d(x1))) -> c#(x1)
      c#(c(x1)) -> d#(d(x1))
      d#(d(x1)) -> c#(f(x1))
      c#(c(x1)) -> d#(x1)
      d#(d(x1)) -> f#(x1)
     TRS:
      b(b(x1)) -> c(d(x1))
      c(c(x1)) -> d(d(d(x1)))
      c(x1) -> g(x1)
      d(d(x1)) -> c(f(x1))
      d(d(d(x1))) -> g(c(x1))
      f(x1) -> a(g(x1))
      g(x1) -> d(a(b(x1)))
      g(g(x1)) -> b(c(x1))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [f#](x0) = x0 + 16,
       
       [g#](x0) = x0 + 14,
       
       [c#](x0) = x0 + 16,
       
       [d#](x0) = x0 + 9,
       
       [b#](x0) = x0 + 13,
       
       [a](x0) = 2,
       
       [f](x0) = x0 + 4,
       
       [g](x0) = x0 + 18,
       
       [c](x0) = x0 + 18,
       
       [d](x0) = x0 + 12,
       
       [b](x0) = x0 + 16
      orientation:
       f#(x1) = x1 + 16 >= x1 + 14 = g#(x1)
       
       g#(g(x1)) = x1 + 32 >= x1 + 31 = b#(c(x1))
       
       b#(b(x1)) = x1 + 29 >= x1 + 28 = c#(d(x1))
       
       c#(x1) = x1 + 16 >= x1 + 14 = g#(x1)
       
       g#(g(x1)) = x1 + 32 >= x1 + 16 = c#(x1)
       
       c#(c(x1)) = x1 + 34 >= x1 + 33 = d#(d(d(x1)))
       
       d#(d(d(x1))) = x1 + 33 >= x1 + 32 = g#(c(x1))
       
       g#(x1) = x1 + 14 >= x1 + 13 = b#(x1)
       
       b#(b(x1)) = x1 + 29 >= x1 + 9 = d#(x1)
       
       d#(d(d(x1))) = x1 + 33 >= x1 + 16 = c#(x1)
       
       c#(c(x1)) = x1 + 34 >= x1 + 21 = d#(d(x1))
       
       d#(d(x1)) = x1 + 21 >= x1 + 20 = c#(f(x1))
       
       c#(c(x1)) = x1 + 34 >= x1 + 9 = d#(x1)
       
       d#(d(x1)) = x1 + 21 >= x1 + 16 = f#(x1)
       
       b(b(x1)) = x1 + 32 >= x1 + 30 = c(d(x1))
       
       c(c(x1)) = x1 + 36 >= x1 + 36 = d(d(d(x1)))
       
       c(x1) = x1 + 18 >= x1 + 18 = g(x1)
       
       d(d(x1)) = x1 + 24 >= x1 + 22 = c(f(x1))
       
       d(d(d(x1))) = x1 + 36 >= x1 + 36 = g(c(x1))
       
       f(x1) = x1 + 4 >= 2 = a(g(x1))
       
       g(x1) = x1 + 18 >= 14 = d(a(b(x1)))
       
       g(g(x1)) = x1 + 36 >= x1 + 34 = b(c(x1))
      problem:
       DPs:
        
       TRS:
        b(b(x1)) -> c(d(x1))
        c(c(x1)) -> d(d(d(x1)))
        c(x1) -> g(x1)
        d(d(x1)) -> c(f(x1))
        d(d(d(x1))) -> g(c(x1))
        f(x1) -> a(g(x1))
        g(x1) -> d(a(b(x1)))
        g(g(x1)) -> b(c(x1))
      Qed