MAYBE

Problem:
 app(app(add(),0()),y) -> y
 app(app(add(),app(s(),x)),y) -> app(s(),app(app(add(),x),y))
 app(app(mult(),0()),y) -> 0()
 app(app(mult(),app(s(),x)),y) -> app(app(add(),app(app(mult(),x),y)),y)
 app(app(app(rec(),f),x),0()) -> x
 app(app(app(rec(),f),x),app(s(),y)) -> app(app(f,app(s(),y)),app(app(app(rec(),f),x),y))
 fact() -> app(app(rec(),mult()),app(s(),0()))

Proof:
 DP Processor:
  DPs:
   app#(app(add(),app(s(),x)),y) -> app#(add(),x)
   app#(app(add(),app(s(),x)),y) -> app#(app(add(),x),y)
   app#(app(add(),app(s(),x)),y) -> app#(s(),app(app(add(),x),y))
   app#(app(mult(),app(s(),x)),y) -> app#(mult(),x)
   app#(app(mult(),app(s(),x)),y) -> app#(app(mult(),x),y)
   app#(app(mult(),app(s(),x)),y) -> app#(add(),app(app(mult(),x),y))
   app#(app(mult(),app(s(),x)),y) -> app#(app(add(),app(app(mult(),x),y)),y)
   app#(app(app(rec(),f),x),app(s(),y)) -> app#(app(app(rec(),f),x),y)
   app#(app(app(rec(),f),x),app(s(),y)) -> app#(f,app(s(),y))
   app#(app(app(rec(),f),x),app(s(),y)) -> app#(app(f,app(s(),y)),app(app(app(rec(),f),x),y))
   fact#() -> app#(s(),0())
   fact#() -> app#(rec(),mult())
   fact#() -> app#(app(rec(),mult()),app(s(),0()))
  TRS:
   app(app(add(),0()),y) -> y
   app(app(add(),app(s(),x)),y) -> app(s(),app(app(add(),x),y))
   app(app(mult(),0()),y) -> 0()
   app(app(mult(),app(s(),x)),y) -> app(app(add(),app(app(mult(),x),y)),y)
   app(app(app(rec(),f),x),0()) -> x
   app(app(app(rec(),f),x),app(s(),y)) -> app(app(f,app(s(),y)),app(app(app(rec(),f),x),y))
   fact() -> app(app(rec(),mult()),app(s(),0()))
  Usable Rule Processor:
   DPs:
    app#(app(add(),app(s(),x)),y) -> app#(add(),x)
    app#(app(add(),app(s(),x)),y) -> app#(app(add(),x),y)
    app#(app(add(),app(s(),x)),y) -> app#(s(),app(app(add(),x),y))
    app#(app(mult(),app(s(),x)),y) -> app#(mult(),x)
    app#(app(mult(),app(s(),x)),y) -> app#(app(mult(),x),y)
    app#(app(mult(),app(s(),x)),y) -> app#(add(),app(app(mult(),x),y))
    app#(app(mult(),app(s(),x)),y) -> app#(app(add(),app(app(mult(),x),y)),y)
    app#(app(app(rec(),f),x),app(s(),y)) -> app#(app(app(rec(),f),x),y)
    app#(app(app(rec(),f),x),app(s(),y)) -> app#(f,app(s(),y))
    app#(app(app(rec(),f),x),app(s(),y)) -> app#(app(f,app(s(),y)),app(app(app(rec(),f),x),y))
    fact#() -> app#(s(),0())
    fact#() -> app#(rec(),mult())
    fact#() -> app#(app(rec(),mult()),app(s(),0()))
   TRS:
    app(app(add(),0()),y) -> y
    app(app(add(),app(s(),x)),y) -> app(s(),app(app(add(),x),y))
    app(app(mult(),0()),y) -> 0()
    app(app(mult(),app(s(),x)),y) -> app(app(add(),app(app(mult(),x),y)),y)
    app(app(app(rec(),f),x),0()) -> x
    app(app(app(rec(),f),x),app(s(),y)) -> app(app(f,app(s(),y)),app(app(app(rec(),f),x),y))
   Open