YES

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> g#(d(x1))
   b#(b(b(x1))) -> c#(x1)
   b#(b(b(x1))) -> c#(d(c(x1)))
   b#(b(x1)) -> g#(x1)
   b#(b(x1)) -> g#(g(x1))
   b#(b(x1)) -> a#(g(g(x1)))
   c#(d(x1)) -> g#(x1)
   c#(d(x1)) -> g#(g(x1))
   g#(g(g(x1))) -> b#(x1)
   g#(g(g(x1))) -> b#(b(x1))
  TRS:
   a(x1) -> g(d(x1))
   b(b(b(x1))) -> c(d(c(x1)))
   b(b(x1)) -> a(g(g(x1)))
   c(d(x1)) -> g(g(x1))
   g(g(g(x1))) -> b(b(x1))
  TDG Processor:
   DPs:
    a#(x1) -> g#(d(x1))
    b#(b(b(x1))) -> c#(x1)
    b#(b(b(x1))) -> c#(d(c(x1)))
    b#(b(x1)) -> g#(x1)
    b#(b(x1)) -> g#(g(x1))
    b#(b(x1)) -> a#(g(g(x1)))
    c#(d(x1)) -> g#(x1)
    c#(d(x1)) -> g#(g(x1))
    g#(g(g(x1))) -> b#(x1)
    g#(g(g(x1))) -> b#(b(x1))
   TRS:
    a(x1) -> g(d(x1))
    b(b(b(x1))) -> c(d(c(x1)))
    b(b(x1)) -> a(g(g(x1)))
    c(d(x1)) -> g(g(x1))
    g(g(g(x1))) -> b(b(x1))
   graph:
    c#(d(x1)) -> g#(g(x1)) -> g#(g(g(x1))) -> b#(b(x1))
    c#(d(x1)) -> g#(g(x1)) -> g#(g(g(x1))) -> b#(x1)
    c#(d(x1)) -> g#(x1) -> g#(g(g(x1))) -> b#(b(x1))
    c#(d(x1)) -> g#(x1) -> g#(g(g(x1))) -> b#(x1)
    b#(b(b(x1))) -> c#(d(c(x1))) -> c#(d(x1)) -> g#(g(x1))
    b#(b(b(x1))) -> c#(d(c(x1))) -> c#(d(x1)) -> g#(x1)
    b#(b(b(x1))) -> c#(x1) -> c#(d(x1)) -> g#(g(x1))
    b#(b(b(x1))) -> c#(x1) -> c#(d(x1)) -> g#(x1)
    b#(b(x1)) -> g#(g(x1)) -> g#(g(g(x1))) -> b#(b(x1))
    b#(b(x1)) -> g#(g(x1)) -> g#(g(g(x1))) -> b#(x1)
    b#(b(x1)) -> g#(x1) -> g#(g(g(x1))) -> b#(b(x1))
    b#(b(x1)) -> g#(x1) -> g#(g(g(x1))) -> b#(x1)
    b#(b(x1)) -> a#(g(g(x1))) -> a#(x1) -> g#(d(x1))
    g#(g(g(x1))) -> b#(b(x1)) -> b#(b(x1)) -> a#(g(g(x1)))
    g#(g(g(x1))) -> b#(b(x1)) -> b#(b(x1)) -> g#(g(x1))
    g#(g(g(x1))) -> b#(b(x1)) -> b#(b(x1)) -> g#(x1)
    g#(g(g(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(d(c(x1)))
    g#(g(g(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(x1)
    g#(g(g(x1))) -> b#(x1) -> b#(b(x1)) -> a#(g(g(x1)))
    g#(g(g(x1))) -> b#(x1) -> b#(b(x1)) -> g#(g(x1))
    g#(g(g(x1))) -> b#(x1) -> b#(b(x1)) -> g#(x1)
    g#(g(g(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(d(c(x1)))
    g#(g(g(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
    a#(x1) -> g#(d(x1)) -> g#(g(g(x1))) -> b#(b(x1))
    a#(x1) -> g#(d(x1)) -> g#(g(g(x1))) -> b#(x1)
   EDG Processor:
    DPs:
     a#(x1) -> g#(d(x1))
     b#(b(b(x1))) -> c#(x1)
     b#(b(b(x1))) -> c#(d(c(x1)))
     b#(b(x1)) -> g#(x1)
     b#(b(x1)) -> g#(g(x1))
     b#(b(x1)) -> a#(g(g(x1)))
     c#(d(x1)) -> g#(x1)
     c#(d(x1)) -> g#(g(x1))
     g#(g(g(x1))) -> b#(x1)
     g#(g(g(x1))) -> b#(b(x1))
    TRS:
     a(x1) -> g(d(x1))
     b(b(b(x1))) -> c(d(c(x1)))
     b(b(x1)) -> a(g(g(x1)))
     c(d(x1)) -> g(g(x1))
     g(g(g(x1))) -> b(b(x1))
    graph:
     c#(d(x1)) -> g#(g(x1)) -> g#(g(g(x1))) -> b#(x1)
     c#(d(x1)) -> g#(g(x1)) -> g#(g(g(x1))) -> b#(b(x1))
     c#(d(x1)) -> g#(x1) -> g#(g(g(x1))) -> b#(x1)
     c#(d(x1)) -> g#(x1) -> g#(g(g(x1))) -> b#(b(x1))
     b#(b(b(x1))) -> c#(d(c(x1))) -> c#(d(x1)) -> g#(x1)
     b#(b(b(x1))) -> c#(d(c(x1))) -> c#(d(x1)) -> g#(g(x1))
     b#(b(b(x1))) -> c#(x1) -> c#(d(x1)) -> g#(x1)
     b#(b(b(x1))) -> c#(x1) -> c#(d(x1)) -> g#(g(x1))
     b#(b(x1)) -> g#(g(x1)) -> g#(g(g(x1))) -> b#(x1)
     b#(b(x1)) -> g#(g(x1)) -> g#(g(g(x1))) -> b#(b(x1))
     b#(b(x1)) -> g#(x1) -> g#(g(g(x1))) -> b#(x1)
     b#(b(x1)) -> g#(x1) -> g#(g(g(x1))) -> b#(b(x1))
     b#(b(x1)) -> a#(g(g(x1))) -> a#(x1) -> g#(d(x1))
     g#(g(g(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(x1)
     g#(g(g(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(d(c(x1)))
     g#(g(g(x1))) -> b#(b(x1)) -> b#(b(x1)) -> g#(x1)
     g#(g(g(x1))) -> b#(b(x1)) -> b#(b(x1)) -> g#(g(x1))
     g#(g(g(x1))) -> b#(b(x1)) -> b#(b(x1)) -> a#(g(g(x1)))
     g#(g(g(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
     g#(g(g(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(d(c(x1)))
     g#(g(g(x1))) -> b#(x1) -> b#(b(x1)) -> g#(x1)
     g#(g(g(x1))) -> b#(x1) -> b#(b(x1)) -> g#(g(x1))
     g#(g(g(x1))) -> b#(x1) -> b#(b(x1)) -> a#(g(g(x1)))
    SCC Processor:
     #sccs: 1
     #rules: 8
     #arcs: 23/100
     DPs:
      c#(d(x1)) -> g#(g(x1))
      g#(g(g(x1))) -> b#(b(x1))
      b#(b(x1)) -> g#(g(x1))
      g#(g(g(x1))) -> b#(x1)
      b#(b(x1)) -> g#(x1)
      b#(b(b(x1))) -> c#(d(c(x1)))
      c#(d(x1)) -> g#(x1)
      b#(b(b(x1))) -> c#(x1)
     TRS:
      a(x1) -> g(d(x1))
      b(b(b(x1))) -> c(d(c(x1)))
      b(b(x1)) -> a(g(g(x1)))
      c(d(x1)) -> g(g(x1))
      g(g(g(x1))) -> b(b(x1))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [c#](x0) = 4x0 + 17,
       
       [b#](x0) = 4x0 + 4,
       
       [g#](x0) = 4x0,
       
       [c](x0) = x0 + 8,
       
       [b](x0) = x0 + 6,
       
       [g](x0) = x0 + 4,
       
       [d](x0) = x0,
       
       [a](x0) = x0 + 4
      orientation:
       c#(d(x1)) = 4x1 + 17 >= 4x1 + 16 = g#(g(x1))
       
       g#(g(g(x1))) = 4x1 + 32 >= 4x1 + 28 = b#(b(x1))
       
       b#(b(x1)) = 4x1 + 28 >= 4x1 + 16 = g#(g(x1))
       
       g#(g(g(x1))) = 4x1 + 32 >= 4x1 + 4 = b#(x1)
       
       b#(b(x1)) = 4x1 + 28 >= 4x1 = g#(x1)
       
       b#(b(b(x1))) = 4x1 + 52 >= 4x1 + 49 = c#(d(c(x1)))
       
       c#(d(x1)) = 4x1 + 17 >= 4x1 = g#(x1)
       
       b#(b(b(x1))) = 4x1 + 52 >= 4x1 + 17 = c#(x1)
       
       a(x1) = x1 + 4 >= x1 + 4 = g(d(x1))
       
       b(b(b(x1))) = x1 + 18 >= x1 + 16 = c(d(c(x1)))
       
       b(b(x1)) = x1 + 12 >= x1 + 12 = a(g(g(x1)))
       
       c(d(x1)) = x1 + 8 >= x1 + 8 = g(g(x1))
       
       g(g(g(x1))) = x1 + 12 >= x1 + 12 = b(b(x1))
      problem:
       DPs:
        
       TRS:
        a(x1) -> g(d(x1))
        b(b(b(x1))) -> c(d(c(x1)))
        b(b(x1)) -> a(g(g(x1)))
        c(d(x1)) -> g(g(x1))
        g(g(g(x1))) -> b(b(x1))
      Qed