YES
We show the termination of the TRS R:

  f(s(x),y,y) -> f(y,x,s(x))


-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: f#(s(x),y,y) -> f#(y,x,s(x))

and R consists of:

r1: f(s(x),y,y) -> f(y,x,s(x))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: f#(s(x),y,y) -> f#(y,x,s(x))

and R consists of:

r1: f(s(x),y,y) -> f(y,x,s(x))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  generalized weighted path order (>=MG, >G)
  
    base order 1:
  
      max/plus interpretation on natural numbers:
      
        f#_A(x1,x2,x3) = max{x1 + 5, x2 + 6, x3 + 4}
        s_A(x1) = max{8, x1 + 2}
  
    base order 2:
  
      marked-algebra reduction triple (>=A, >=A!, >A!):
      
        matrix interpretation with standard point-wise order:
        
          carrier: N^1
          order: standard order
          interpretations:
            f#_A(x1,x2,x3) = 0
            s_A(x1) = x1 + 1
            f#!_A(x1,x2,x3) = x1 + x2 + 2
            s!_A(x1) = x1 + 1
  
    partial status:
  
      pi(f#) = []
      pi(s) = [1]

The following rules are removed:

  p1

Then no dependency pair remains.