YES

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

  f(g(x)) -> g(f(f(x)))
  f(h(x)) -> h(g(x))
  f'(s(x),y,y) -> f'(y,x,s(x))

and S is:

  rand(x) -> x
  rand(x) -> rand(s(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#(g(x)) -> f#(f(x))
  f#(g(x)) -> f#(x)
  f'#(s(x),y,y) -> f'#(y,x,s(x))

and Q consists of the rules:

  f(g(x)) -> g(f(f(x)))
  f(h(x)) -> h(g(x))
  f'(s(x),y,y) -> f'(y,x,s(x))
  rand(x) -> x
  rand(x) -> rand(s(x))

The weakly monotone algebra (N^2, >_lex) with

  f#_A((x1,y1)) = (0, 0)
  g_A((x1,y1)) = (1, 1)
  f_A((x1,y1)) = (3, 0)
  f'#_A((x1,y1),(x2,y2),(x3,y3)) = (x1 + x2, y1 + y2)
  s_A((x1,y1)) = (x1, y1 + 1)
  h_A((x1,y1)) = (x1 + 1, y1)
  f'_A((x1,y1),(x2,y2),(x3,y3)) = (x1 + x3, y1 + y3)
  rand_A((x1,y1)) = (x1 + 1, 0)

strictly orients the following dependency pairs:

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

We remove them from the set of dependency pairs.

The weakly monotone algebra (N^2, >_lex) with

  f#_A((x1,y1)) = (x1, y1)
  g_A((x1,y1)) = (x1, y1 + 1)
  f_A((x1,y1)) = (x1, y1)
  h_A((x1,y1)) = (x1 + 1, 1)
  f'_A((x1,y1),(x2,y2),(x3,y3)) = (x1 + x3, y1 + y3)
  s_A((x1,y1)) = (x1, y1)
  rand_A((x1,y1)) = (x1 + 1, y1)

strictly orients the following dependency pairs:

  f#(g(x)) -> f#(f(x))
  f#(g(x)) -> f#(x)

We remove them from the set of dependency pairs.

No dependency pair remains.