YES

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

Proof:
 DP Processor:
  DPs:
   f#(a()) -> f#(c(a()))
   f#(c(a())) -> f#(d(b()))
   f#(a()) -> f#(d(a()))
   f#(c(b())) -> f#(d(a()))
   e#(g(X)) -> e#(X)
  TRS:
   f(a()) -> f(c(a()))
   f(c(X)) -> X
   f(c(a())) -> f(d(b()))
   f(a()) -> f(d(a()))
   f(d(X)) -> X
   f(c(b())) -> f(d(a()))
   e(g(X)) -> e(X)
  TDG Processor:
   DPs:
    f#(a()) -> f#(c(a()))
    f#(c(a())) -> f#(d(b()))
    f#(a()) -> f#(d(a()))
    f#(c(b())) -> f#(d(a()))
    e#(g(X)) -> e#(X)
   TRS:
    f(a()) -> f(c(a()))
    f(c(X)) -> X
    f(c(a())) -> f(d(b()))
    f(a()) -> f(d(a()))
    f(d(X)) -> X
    f(c(b())) -> f(d(a()))
    e(g(X)) -> e(X)
   graph:
    e#(g(X)) -> e#(X) -> e#(g(X)) -> e#(X)
    f#(c(b())) -> f#(d(a())) -> f#(c(b())) -> f#(d(a()))
    f#(c(b())) -> f#(d(a())) -> f#(a()) -> f#(d(a()))
    f#(c(b())) -> f#(d(a())) -> f#(c(a())) -> f#(d(b()))
    f#(c(b())) -> f#(d(a())) -> f#(a()) -> f#(c(a()))
    f#(c(a())) -> f#(d(b())) -> f#(c(b())) -> f#(d(a()))
    f#(c(a())) -> f#(d(b())) -> f#(a()) -> f#(d(a()))
    f#(c(a())) -> f#(d(b())) -> f#(c(a())) -> f#(d(b()))
    f#(c(a())) -> f#(d(b())) -> f#(a()) -> f#(c(a()))
    f#(a()) -> f#(d(a())) -> f#(c(b())) -> f#(d(a()))
    f#(a()) -> f#(d(a())) -> f#(a()) -> f#(d(a()))
    f#(a()) -> f#(d(a())) -> f#(c(a())) -> f#(d(b()))
    f#(a()) -> f#(d(a())) -> f#(a()) -> f#(c(a()))
    f#(a()) -> f#(c(a())) -> f#(c(b())) -> f#(d(a()))
    f#(a()) -> f#(c(a())) -> f#(a()) -> f#(d(a()))
    f#(a()) -> f#(c(a())) -> f#(c(a())) -> f#(d(b()))
    f#(a()) -> f#(c(a())) -> f#(a()) -> f#(c(a()))
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 17/25
    DPs:
     f#(c(b())) -> f#(d(a()))
     f#(a()) -> f#(c(a()))
     f#(c(a())) -> f#(d(b()))
     f#(a()) -> f#(d(a()))
    TRS:
     f(a()) -> f(c(a()))
     f(c(X)) -> X
     f(c(a())) -> f(d(b()))
     f(a()) -> f(d(a()))
     f(d(X)) -> X
     f(c(b())) -> f(d(a()))
     e(g(X)) -> e(X)
    EDG Processor:
     DPs:
      f#(c(b())) -> f#(d(a()))
      f#(a()) -> f#(c(a()))
      f#(c(a())) -> f#(d(b()))
      f#(a()) -> f#(d(a()))
     TRS:
      f(a()) -> f(c(a()))
      f(c(X)) -> X
      f(c(a())) -> f(d(b()))
      f(a()) -> f(d(a()))
      f(d(X)) -> X
      f(c(b())) -> f(d(a()))
      e(g(X)) -> e(X)
     graph:
      f#(a()) -> f#(c(a())) -> f#(c(a())) -> f#(d(b()))
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 1/16
      
    
    DPs:
     e#(g(X)) -> e#(X)
    TRS:
     f(a()) -> f(c(a()))
     f(c(X)) -> X
     f(c(a())) -> f(d(b()))
     f(a()) -> f(d(a()))
     f(d(X)) -> X
     f(c(b())) -> f(d(a()))
     e(g(X)) -> e(X)
    Subterm Criterion Processor:
     simple projection:
      pi(e#) = 0
     problem:
      DPs:
       
      TRS:
       f(a()) -> f(c(a()))
       f(c(X)) -> X
       f(c(a())) -> f(d(b()))
       f(a()) -> f(d(a()))
       f(d(X)) -> X
       f(c(b())) -> f(d(a()))
       e(g(X)) -> e(X)
     Qed