YES
Time: 0.009011
TRS:
 {f c(X, s Y) -> f c(s X, Y),
  g c(s X, Y) -> f c(X, s Y)}
 DP:
  DP:
   {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)}
  UR:
   {}
   EDG:
    {(f# c(X, s Y) -> f# c(s X, Y), f# c(X, s Y) -> f# c(s X, Y))
     (g# c(s X, Y) -> f# c(X, s Y), f# c(X, s Y) -> f# c(s X, Y))}
    STATUS:
     arrows: 0.500000
     SCCS (1):
      Scc:
       {f# c(X, s Y) -> f# c(s X, Y)}
      
      
      SCC (1):
       Strict:
        {f# c(X, s Y) -> f# c(s X, Y)}
       Weak:
       {f c(X, s Y) -> f c(s X, Y),
        g c(s X, Y) -> f c(X, s Y)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [c](x0, x1) = x0,
         
         [f](x0) = 0,
         
         [s](x0) = x0 + 1,
         
         [g](x0) = 0,
         
         [f#](x0) = x0
        Strict:
         f# c(X, s Y) -> f# c(s X, Y)
         1 + 0X + 1Y >= 0 + 0X + 1Y
        Weak:
         g c(s X, Y) -> f c(X, s Y)
         0 + 0X + 0Y >= 0 + 0X + 0Y
         f c(X, s Y) -> f c(s X, Y)
         0 + 0X + 0Y >= 0 + 0X + 0Y
       Qed