YES

Problem:
 f(0(x1)) -> s(0(x1))
 d(0(x1)) -> 0(x1)
 d(s(x1)) -> s(s(d(x1)))
 f(s(x1)) -> d(f(x1))

Proof:
 DP Processor:
  DPs:
   d#(s(x1)) -> d#(x1)
   f#(s(x1)) -> f#(x1)
   f#(s(x1)) -> d#(f(x1))
  TRS:
   f(0(x1)) -> s(0(x1))
   d(0(x1)) -> 0(x1)
   d(s(x1)) -> s(s(d(x1)))
   f(s(x1)) -> d(f(x1))
  TDG Processor:
   DPs:
    d#(s(x1)) -> d#(x1)
    f#(s(x1)) -> f#(x1)
    f#(s(x1)) -> d#(f(x1))
   TRS:
    f(0(x1)) -> s(0(x1))
    d(0(x1)) -> 0(x1)
    d(s(x1)) -> s(s(d(x1)))
    f(s(x1)) -> d(f(x1))
   graph:
    d#(s(x1)) -> d#(x1) -> d#(s(x1)) -> d#(x1)
    f#(s(x1)) -> d#(f(x1)) -> d#(s(x1)) -> d#(x1)
    f#(s(x1)) -> f#(x1) -> f#(s(x1)) -> d#(f(x1))
    f#(s(x1)) -> f#(x1) -> f#(s(x1)) -> f#(x1)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 4/9
    DPs:
     f#(s(x1)) -> f#(x1)
    TRS:
     f(0(x1)) -> s(0(x1))
     d(0(x1)) -> 0(x1)
     d(s(x1)) -> s(s(d(x1)))
     f(s(x1)) -> d(f(x1))
    LPO Processor:
     argument filtering:
      pi(0) = 0
      pi(f) = [0]
      pi(s) = [0]
      pi(d) = [0]
      pi(f#) = [0]
     precedence:
      f > d > f# ~ s ~ 0
     problem:
      DPs:
       
      TRS:
       f(0(x1)) -> s(0(x1))
       d(0(x1)) -> 0(x1)
       d(s(x1)) -> s(s(d(x1)))
       f(s(x1)) -> d(f(x1))
     Qed
    
    DPs:
     d#(s(x1)) -> d#(x1)
    TRS:
     f(0(x1)) -> s(0(x1))
     d(0(x1)) -> 0(x1)
     d(s(x1)) -> s(s(d(x1)))
     f(s(x1)) -> d(f(x1))
    LPO Processor:
     argument filtering:
      pi(0) = 0
      pi(f) = [0]
      pi(s) = [0]
      pi(d) = [0]
      pi(d#) = [0]
     precedence:
      f > d > d# ~ s ~ 0
     problem:
      DPs:
       
      TRS:
       f(0(x1)) -> s(0(x1))
       d(0(x1)) -> 0(x1)
       d(s(x1)) -> s(s(d(x1)))
       f(s(x1)) -> d(f(x1))
     Qed