YES

---- CR(R)
---- Hot decreasingness.
R:
h(f(f(c())),b()) -> f(h(h(h(c(),h(f(h(c(),f(b()))),a())),b()),c()))
c() -> c()
f(f(h(h(f(a()),a()),c()))) -> f(h(f(c()),b()))
h(f(h(f(b()),h(h(f(h(c(),f(c()))),b()),a()))),h(a(),c())) -> c()

C:
h(f(f(c())),b()) -> f(h(h(h(c(),h(f(h(c(),f(b()))),a())),b()),c()))
f(f(h(h(f(a()),a()),c()))) -> f(h(f(c()),b()))
h(f(h(f(b()),h(h(f(h(c(),f(c()))),b()),a()))),h(a(),c())) -> c()

Label:
[c() -> c()] = 0