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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f#](x0) = 8x0 + 16,
    
    [g#](x0) = 8x0 + 15,
    
    [c#](x0) = 8x0 + 20,
    
    [d#](x0) = 8x0 + 10,
    
    [b#](x0) = 8x0 + 13,
    
    [a](x0) = 0,
    
    [f](x0) = x0,
    
    [g](x0) = x0 + 3,
    
    [c](x0) = x0 + 3,
    
    [d](x0) = x0 + 2,
    
    [b](x0) = x0 + 3
   orientation:
    b#(b(x1)) = 8x1 + 37 >= 8x1 + 10 = d#(x1)
    
    b#(b(x1)) = 8x1 + 37 >= 8x1 + 36 = c#(d(x1))
    
    c#(c(x1)) = 8x1 + 44 >= 8x1 + 10 = d#(x1)
    
    c#(c(x1)) = 8x1 + 44 >= 8x1 + 26 = d#(d(x1))
    
    c#(c(x1)) = 8x1 + 44 >= 8x1 + 42 = d#(d(d(x1)))
    
    c#(x1) = 8x1 + 20 >= 8x1 + 15 = g#(x1)
    
    d#(d(x1)) = 8x1 + 26 >= 8x1 + 16 = f#(x1)
    
    d#(d(x1)) = 8x1 + 26 >= 8x1 + 20 = c#(f(x1))
    
    d#(d(d(x1))) = 8x1 + 42 >= 8x1 + 20 = c#(x1)
    
    d#(d(d(x1))) = 8x1 + 42 >= 8x1 + 39 = g#(c(x1))
    
    f#(x1) = 8x1 + 16 >= 8x1 + 15 = g#(x1)
    
    g#(x1) = 8x1 + 15 >= 8x1 + 13 = b#(x1)
    
    g#(x1) = 8x1 + 15 >= 10 = d#(a(b(x1)))
    
    g#(g(x1)) = 8x1 + 39 >= 8x1 + 20 = c#(x1)
    
    g#(g(x1)) = 8x1 + 39 >= 8x1 + 37 = b#(c(x1))
    
    b(b(x1)) = x1 + 6 >= x1 + 5 = c(d(x1))
    
    c(c(x1)) = x1 + 6 >= x1 + 6 = d(d(d(x1)))
    
    c(x1) = x1 + 3 >= x1 + 3 = g(x1)
    
    d(d(x1)) = x1 + 4 >= x1 + 3 = c(f(x1))
    
    d(d(d(x1))) = x1 + 6 >= x1 + 6 = g(c(x1))
    
    f(x1) = x1 >= 0 = a(g(x1))
    
    g(x1) = x1 + 3 >= 2 = d(a(b(x1)))
    
    g(g(x1)) = x1 + 6 >= x1 + 6 = 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