YES

Problem:
 f(c(X,s(Y))) -> f(c(s(X),Y))
 g(c(s(X),Y)) -> f(c(X,s(Y)))

Proof:
 DP Processor:
  DPs:
   f#(c(X,s(Y))) -> f#(c(s(X),Y))
   g#(c(s(X),Y)) -> f#(c(X,s(Y)))
  TRS:
   f(c(X,s(Y))) -> f(c(s(X),Y))
   g(c(s(X),Y)) -> f(c(X,s(Y)))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [g#](x0) = 7x0 + 2,
    
    [f#](x0) = x0,
    
    [g](x0) = 7x0 + -16,
    
    [f](x0) = x0,
    
    [c](x0, x1) = x1,
    
    [s](x0) = 6x0
   orientation:
    f#(c(X,s(Y))) = 6Y >= Y = f#(c(s(X),Y))
    
    g#(c(s(X),Y)) = 7Y + 2 >= 6Y = f#(c(X,s(Y)))
    
    f(c(X,s(Y))) = 6Y >= Y = f(c(s(X),Y))
    
    g(c(s(X),Y)) = 7Y + -16 >= 6Y = f(c(X,s(Y)))
   problem:
    DPs:
     
    TRS:
     f(c(X,s(Y))) -> f(c(s(X),Y))
     g(c(s(X),Y)) -> f(c(X,s(Y)))
   Qed