YES

Problem:
 f(s(x)) -> s(f(f(x)))
 f(x) -> c(x,x)

Proof:
 DP Processor:
  DPs:
   f#(s(x)) -> f#(x)
   f#(s(x)) -> f#(f(x))
  TRS:
   f(s(x)) -> s(f(f(x)))
   f(x) -> c(x,x)
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [f#](x0) = 1x0,
    
    [c](x0, x1) = -16x0 + x1,
    
    [f](x0) = x0,
    
    [s](x0) = 3x0
   orientation:
    f#(s(x)) = 4x >= 1x = f#(x)
    
    f#(s(x)) = 4x >= 1x = f#(f(x))
    
    f(s(x)) = 3x >= 3x = s(f(f(x)))
    
    f(x) = x >= x = c(x,x)
   problem:
    DPs:
     
    TRS:
     f(s(x)) -> s(f(f(x)))
     f(x) -> c(x,x)
   Qed