YES
TRS:
 {   f(X, X) -> c(X),
  f(X, c(X)) -> f(s(X), X),
  f(s(X), X) -> f(X, a(X))}
 DP:
  Strict:
   {f#(X, c(X)) -> f#(s(X), X),
    f#(s(X), X) -> f#(X, a(X))}
  Weak:
  {   f(X, X) -> c(X),
   f(X, c(X)) -> f(s(X), X),
   f(s(X), X) -> f(X, a(X))}
  EDG:
   {(f#(s(X), X) -> f#(X, a(X)), f#(s(X), X) -> f#(X, a(X)))
    (f#(X, c(X)) -> f#(s(X), X), f#(X, c(X)) -> f#(s(X), X))
    (f#(X, c(X)) -> f#(s(X), X), f#(s(X), X) -> f#(X, a(X)))}
   SCCS:
    Scc:
     {f#(s(X), X) -> f#(X, a(X))}
    Scc:
     {f#(X, c(X)) -> f#(s(X), X)}
    SCC:
     Strict:
      {f#(s(X), X) -> f#(X, a(X))}
     Weak:
     {   f(X, X) -> c(X),
      f(X, c(X)) -> f(s(X), X),
      f(s(X), X) -> f(X, a(X))}
     SPSC:
      Simple Projection:
       pi(f#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {f#(X, c(X)) -> f#(s(X), X)}
     Weak:
     {   f(X, X) -> c(X),
      f(X, c(X)) -> f(s(X), X),
      f(s(X), X) -> f(X, a(X))}
     SPSC:
      Simple Projection:
       pi(f#) = 1
      Strict:
       {}
      Qed