YES

We show the termination of R/S, where R is

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

and S is:

  f(x,y) -> f(l(x),y)
  f(x,y) -> f(x,r(y))
  l(el(x)) -> el(l(x))
  el(r(x)) -> r(el(x))

Since R almost dominates S and S is non-duplicating,
it is enough to show finiteness of (P, Q).
Here P consists of the dependency pairs

  f#(el(x),y) -> f#(x,el(y))

and Q consists of the rules:

  f(el(x),y) -> f(x,el(y))
  f(x,y) -> f(l(x),y)
  f(x,y) -> f(x,r(y))
  l(el(x)) -> el(l(x))
  el(r(x)) -> r(el(x))
  f#(x,y) -> f#(l(x),y)
  f#(x,y) -> f#(x,r(y))

The weakly monotone algebra (N, >) with

  f#_A(x1,x2) = x1
  el_A(x1) = x1 + 1
  f_A(x1,x2) = x1
  l_A(x1) = x1
  r_A(x1) = x1 + 1

strictly orients the following dependency pairs:

  f#(el(x),y) -> f#(x,el(y))

We remove them from the set of dependency pairs.

No dependency pair remains.