YES

Problem:
 f(s(X),X) -> f(X,a(X))
 f(X,c(X)) -> f(s(X),X)
 f(X,X) -> c(X)

Proof:
 DP Processor:
  DPs:
   f#(s(X),X) -> f#(X,a(X))
   f#(X,c(X)) -> f#(s(X),X)
  TRS:
   f(s(X),X) -> f(X,a(X))
   f(X,c(X)) -> f(s(X),X)
   f(X,X) -> c(X)
  EDG Processor:
   DPs:
    f#(s(X),X) -> f#(X,a(X))
    f#(X,c(X)) -> f#(s(X),X)
   TRS:
    f(s(X),X) -> f(X,a(X))
    f(X,c(X)) -> f(s(X),X)
    f(X,X) -> c(X)
   graph:
    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#(s(X),X) -> f#(X,a(X))
    f#(X,c(X)) -> f#(s(X),X) -> f#(X,c(X)) -> f#(s(X),X)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 3/4
    DPs:
     f#(X,c(X)) -> f#(s(X),X)
    TRS:
     f(s(X),X) -> f(X,a(X))
     f(X,c(X)) -> f(s(X),X)
     f(X,X) -> c(X)
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 1
     problem:
      DPs:
       
      TRS:
       f(s(X),X) -> f(X,a(X))
       f(X,c(X)) -> f(s(X),X)
       f(X,X) -> c(X)
     Qed
    
    DPs:
     f#(s(X),X) -> f#(X,a(X))
    TRS:
     f(s(X),X) -> f(X,a(X))
     f(X,c(X)) -> f(s(X),X)
     f(X,X) -> c(X)
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 0
     problem:
      DPs:
       
      TRS:
       f(s(X),X) -> f(X,a(X))
       f(X,c(X)) -> f(s(X),X)
       f(X,X) -> c(X)
     Qed