YES

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

Proof:
 Church Rosser Transformation Processor (critical pair closing system, Thm 2.4):
  strict:
   
  weak:
   c() -> f(a(),h(b()))
   f(h(f(f(a(),a()),h(a()))),g(f(x,g(b())))) -> c()
   c() -> c()
   g(g(a())) -> f(h(g(f(c(),c()))),f(f(g(c()),a()),g(f(a(),a()))))
   f(x,y) -> f(y,x)
  original problem:
   c() -> f(a(),h(b()))
   f(x69,h(x66)) -> f(h(x66),x69)
   f(h(f(f(a(),a()),h(a()))),g(f(x70,g(b())))) -> c()
   f(h(a()),x77) -> f(x77,h(a()))
   f(g(b()),x80) -> f(x80,g(b()))
  critical peaks: 
   Shift Processor (no label):
    c() -> f(a(),h(b()))
    f(x69,h(x66)) -> f(h(x66),x69)
    f(h(f(f(a(),a()),h(a()))),g(f(x70,g(b())))) -> c()
    f(h(a()),x77) -> f(x77,h(a()))
    f(g(b()),x80) -> f(x80,g(b()))
    Church Rosser Transformation Processor (critical pair closing system, Thm 2.4):
     strict:
      
     weak:
      c() -> f(a(),h(b()))
      f(x69,h(x66)) -> f(h(x66),x69)
      f(h(f(f(a(),a()),h(a()))),g(f(x70,g(b())))) -> c()
      f(h(a()),x77) -> f(x77,h(a()))
      f(g(b()),x80) -> f(x80,g(b()))
     original problem:
      f(h(a()),f(a(),a())) -> f(f(a(),a()),h(a()))
      f(h(f(f(a(),a()),h(a()))),g(f(x197,g(b())))) -> c()
      f(g(b()),h(a())) -> f(h(a()),g(b()))
      f(h(f(f(a(),a()),h(a()))),g(f(h(a()),g(b())))) -> c()
      f(h(f(f(a(),a()),h(a()))),g(f(g(b()),g(b())))) -> c()
     critical peaks: 
      Shift Processor (no label):
       f(h(a()),f(a(),a())) -> f(f(a(),a()),h(a()))
       f(h(f(f(a(),a()),h(a()))),g(f(x197,g(b())))) -> c()
       f(g(b()),h(a())) -> f(h(a()),g(b()))
       f(h(f(f(a(),a()),h(a()))),g(f(h(a()),g(b())))) -> c()
       f(h(f(f(a(),a()),h(a()))),g(f(g(b()),g(b())))) -> c()
       Church Rosser Transformation Processor:
        
        critical peaks: joinable
        Qed