MAYBE

Problem:
 app(app(app(if(),true()),x),y) -> x
 app(app(app(if(),false()),x),y) -> y
 app(app(app(until(),p),f),x) -> app(app(app(if(),app(p,x)),x),app(app(app(until(),p),f),app(f,x)))

Proof:
 DP Processor:
  DPs:
   app#(app(app(until(),p),f),x) -> app#(f,x)
   app#(app(app(until(),p),f),x) -> app#(app(app(until(),p),f),app(f,x))
   app#(app(app(until(),p),f),x) -> app#(p,x)
   app#(app(app(until(),p),f),x) -> app#(if(),app(p,x))
   app#(app(app(until(),p),f),x) -> app#(app(if(),app(p,x)),x)
   app#(app(app(until(),p),f),x) ->
   app#(app(app(if(),app(p,x)),x),app(app(app(until(),p),f),app(f,x)))
  TRS:
   app(app(app(if(),true()),x),y) -> x
   app(app(app(if(),false()),x),y) -> y
   app(app(app(until(),p),f),x) ->
   app(app(app(if(),app(p,x)),x),app(app(app(until(),p),f),app(f,x)))
  Open