YES

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

Proof:
 DP Processor:
  DPs:
   d#(s(x1)) -> p#(s(x1))
   d#(s(x1)) -> d#(p(s(x1)))
   f#(s(x1)) -> p#(s(x1))
   f#(s(x1)) -> f#(p(s(x1)))
   f#(s(x1)) -> d#(f(p(s(x1))))
  TRS:
   f(0(x1)) -> s(0(x1))
   d(0(x1)) -> 0(x1)
   d(s(x1)) -> s(s(d(p(s(x1)))))
   f(s(x1)) -> d(f(p(s(x1))))
   p(s(x1)) -> x1
  TDG Processor:
   DPs:
    d#(s(x1)) -> p#(s(x1))
    d#(s(x1)) -> d#(p(s(x1)))
    f#(s(x1)) -> p#(s(x1))
    f#(s(x1)) -> f#(p(s(x1)))
    f#(s(x1)) -> d#(f(p(s(x1))))
   TRS:
    f(0(x1)) -> s(0(x1))
    d(0(x1)) -> 0(x1)
    d(s(x1)) -> s(s(d(p(s(x1)))))
    f(s(x1)) -> d(f(p(s(x1))))
    p(s(x1)) -> x1
   graph:
    d#(s(x1)) -> d#(p(s(x1))) -> d#(s(x1)) -> d#(p(s(x1)))
    d#(s(x1)) -> d#(p(s(x1))) -> d#(s(x1)) -> p#(s(x1))
    f#(s(x1)) -> d#(f(p(s(x1)))) -> d#(s(x1)) -> d#(p(s(x1)))
    f#(s(x1)) -> d#(f(p(s(x1)))) -> d#(s(x1)) -> p#(s(x1))
    f#(s(x1)) -> f#(p(s(x1))) -> f#(s(x1)) -> d#(f(p(s(x1))))
    f#(s(x1)) -> f#(p(s(x1))) -> f#(s(x1)) -> f#(p(s(x1)))
    f#(s(x1)) -> f#(p(s(x1))) -> f#(s(x1)) -> p#(s(x1))
   CDG Processor:
    DPs:
     d#(s(x1)) -> p#(s(x1))
     d#(s(x1)) -> d#(p(s(x1)))
     f#(s(x1)) -> p#(s(x1))
     f#(s(x1)) -> f#(p(s(x1)))
     f#(s(x1)) -> d#(f(p(s(x1))))
    TRS:
     f(0(x1)) -> s(0(x1))
     d(0(x1)) -> 0(x1)
     d(s(x1)) -> s(s(d(p(s(x1)))))
     f(s(x1)) -> d(f(p(s(x1))))
     p(s(x1)) -> x1
    graph:
     f#(s(x1)) -> d#(f(p(s(x1)))) -> d#(s(x1)) -> p#(s(x1))
     f#(s(x1)) -> d#(f(p(s(x1)))) -> d#(s(x1)) -> d#(p(s(x1)))
    SCC Processor:
     #sccs: 0
     #rules: 0
     #arcs: 2/25