YES

Problem:
 a() -> g(c())
 g(a()) -> b()
 f(g(X),b()) -> f(a(),X)

Proof:
 DP Processor:
  DPs:
   a#() -> g#(c())
   f#(g(X),b()) -> a#()
   f#(g(X),b()) -> f#(a(),X)
  TRS:
   a() -> g(c())
   g(a()) -> b()
   f(g(X),b()) -> f(a(),X)
  Usable Rule Processor:
   DPs:
    a#() -> g#(c())
    f#(g(X),b()) -> a#()
    f#(g(X),b()) -> f#(a(),X)
   TRS:
    a() -> g(c())
   EDG Processor:
    DPs:
     a#() -> g#(c())
     f#(g(X),b()) -> a#()
     f#(g(X),b()) -> f#(a(),X)
    TRS:
     a() -> g(c())
    graph:
     f#(g(X),b()) -> f#(a(),X) -> f#(g(X),b()) -> a#()
     f#(g(X),b()) -> f#(a(),X) -> f#(g(X),b()) -> f#(a(),X)
     f#(g(X),b()) -> a#() -> a#() -> g#(c())
    Restore Modifier:
     DPs:
      a#() -> g#(c())
      f#(g(X),b()) -> a#()
      f#(g(X),b()) -> f#(a(),X)
     TRS:
      a() -> g(c())
      g(a()) -> b()
      f(g(X),b()) -> f(a(),X)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 3/9
      DPs:
       f#(g(X),b()) -> f#(a(),X)
      TRS:
       a() -> g(c())
       g(a()) -> b()
       f(g(X),b()) -> f(a(),X)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0, x1) = x0 + x1 + 1,
        
        [f](x0, x1) = x0 + x1 + 1,
        
        [b] = 1,
        
        [g](x0) = x0 + 1,
        
        [c] = 0,
        
        [a] = 1
       orientation:
        f#(g(X),b()) = X + 3 >= X + 2 = f#(a(),X)
        
        a() = 1 >= 1 = g(c())
        
        g(a()) = 2 >= 1 = b()
        
        f(g(X),b()) = X + 3 >= X + 2 = f(a(),X)
       problem:
        DPs:
         
        TRS:
         a() -> g(c())
         g(a()) -> b()
         f(g(X),b()) -> f(a(),X)
       Qed