NO

1 decompositions
 #1 -----------
   2: a() -> f(h(h(f(a()),f(f(c()))),b()))
   3: c() -> a()
   4: h(c(),f(b())) -> c()

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

original is
   1: c() -> c()
   2: a() -> f(h(h(f(a()),f(f(c()))),b()))
   3: c() -> a()
   4: h(c(),f(b())) -> c()

reduced to
   2: a() -> f(h(h(f(a()),f(f(c()))),b()))
   3: c() -> a()
   4: h(c(),f(b())) -> c()