YES

Problem:
 f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
 f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))

Proof:
 DP Processor:
  DPs:
   f#(g(i(a(),b(),b'()),c()),d()) -> f#(.(b'(),c()),d'())
   f#(g(i(a(),b(),b'()),c()),d()) -> f#(.(b(),c()),d'())
   f#(g(h(a(),b()),c()),d()) -> f#(c(),d'())
   f#(g(h(a(),b()),c()),d()) -> f#(.(b(),g(h(a(),b()),c())),d())
  TRS:
   f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
   f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
  EDG Processor:
   DPs:
    f#(g(i(a(),b(),b'()),c()),d()) -> f#(.(b'(),c()),d'())
    f#(g(i(a(),b(),b'()),c()),d()) -> f#(.(b(),c()),d'())
    f#(g(h(a(),b()),c()),d()) -> f#(c(),d'())
    f#(g(h(a(),b()),c()),d()) -> f#(.(b(),g(h(a(),b()),c())),d())
   TRS:
    f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
    f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
   graph:
    
   Qed