NO

1 decompositions
 #1 -----------
   1: g(x1) -> h(k(x1))
   3: h(k(x3)) -> f(x3)
   4: f(x4) -> x4
   5: k(c()) -> c()
   6: f(c()) -> g(c())

unjoinable peak
    c()
*<- f(c()) ->*
    h(c())
NOTE: input TRS is reduced

original is
   1: g(x1) -> h(k(x1))
   2: g(x2) -> x2
   3: h(k(x3)) -> f(x3)
   4: f(x4) -> x4
   5: k(c()) -> c()
   6: f(c()) -> g(c())

reduced to
   1: g(x1) -> h(k(x1))
   3: h(k(x3)) -> f(x3)
   4: f(x4) -> x4
   5: k(c()) -> c()
   6: f(c()) -> g(c())