NO

1 decompositions
 #0 -----------
   1: r(e(x)) -> w(r(x))
   2: i(t(x)) -> e(r(x))
   3: e(w(x)) -> r(i(x))
   4: t(e(x)) -> r(e(x))
   5: w(r(x)) -> i(t(x))
   6: e(r(x)) -> e(w(x))
   7: r(i(t(e(r(x))))) -> e(w(r(i(t(e(x))))))

unjoinable peak
    r(i(r(x)))
*<- e(r(e(x))) ->*
    r(i(e(x)))