YES

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

Proof:
 Uncurry Processor:
  f5(f(),f5(f5(h(),c()),c())) -> a()
  a() -> b()
  f5(f(),b()) -> f5(f(),c())
  c() -> f5(f(),c())
  Ground Confluence Processor:
   UNC by decision procedure.