MAYBE

Problem:
 app(app(app(consif(),true()),x),ys) -> app(app(cons(),x),ys)
 app(app(app(consif(),false()),x),ys) -> ys
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) ->
 app(app(app(consif(),app(f,x)),x),app(app(filter(),f),xs))

Proof:
 DP Processor:
  DPs:
   app#(app(app(consif(),true()),x),ys) -> app#(cons(),x)
   app#(app(app(consif(),true()),x),ys) -> app#(app(cons(),x),ys)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter(),f),xs)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(consif(),app(f,x))
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(consif(),app(f,x)),x)
   app#(app(filter(),f),app(app(cons(),x),xs)) ->
   app#(app(app(consif(),app(f,x)),x),app(app(filter(),f),xs))
  TRS:
   app(app(app(consif(),true()),x),ys) -> app(app(cons(),x),ys)
   app(app(app(consif(),false()),x),ys) -> ys
   app(app(filter(),f),nil()) -> nil()
   app(app(filter(),f),app(app(cons(),x),xs)) ->
   app(app(app(consif(),app(f,x)),x),app(app(filter(),f),xs))
  Open