YES

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

Proof:
 DP Processor:
  DPs:
   f#(a(x),y) -> g#(x,y)
   g#(b(),y) -> f#(y,y)
  TRS:
   f(a(x),y) -> g(x,y)
   g(b(),y) -> f(y,y)
   a(b()) -> c()
  EDG Processor:
   DPs:
    f#(a(x),y) -> g#(x,y)
    g#(b(),y) -> f#(y,y)
   TRS:
    f(a(x),y) -> g(x,y)
    g(b(),y) -> f(y,y)
    a(b()) -> c()
   graph:
    g#(b(),y) -> f#(y,y) -> f#(a(x),y) -> g#(x,y)
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 1/4