MAYBE

Problem:
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),y),ys)) ->
 app(app(app(filtersub(),app(f,y)),f),app(app(cons(),y),ys))
 app(app(app(filtersub(),true()),f),app(app(cons(),y),ys)) ->
 app(app(cons(),y),app(app(filter(),f),ys))
 app(app(app(filtersub(),false()),f),app(app(cons(),y),ys)) -> app(app(filter(),f),ys)

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