YES

1 decompositions
 #0 -----------
   1: max(x,0()) -> x
   2: max(0(),y) -> y
   3: max(s(x),s(y)) -> s(max(x,y))
   4: max(x,y) -> max(y,x)

@Strongly Commuting
--- R
   1: max(x,0()) -> x
   2: max(0(),y) -> y
   3: max(s(x),s(y)) -> s(max(x,y))
   4: max(x,y) -> max(y,x)

--- S
   1: max(x,0()) -> x
   2: max(0(),y) -> y
   3: max(s(x),s(y)) -> s(max(x,y))
   4: max(x,y) -> max(y,x)