NO

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

Proof:
 Uncurry Processor:
  a() -> f5(f(),b())
  f5(f5(h(),b()),f5(f(),c())) -> c()
  b() -> f5(f(),b())
  b() -> f5(f(),c())
  f5(f5(h(),c()),c()) -> c()
  Ground Confluence Processor:
   not UNR by decision procedure.