MAYBE

Problem:
 p(s(x)) -> x
 fact(0()) -> s(0())
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 *(0(),y) -> 0()
 *(s(x),y) -> +(*(x,y),y)
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))

Proof:
 DP Processor:
  DPs:
   fact#(s(x)) -> p#(s(x))
   fact#(s(x)) -> fact#(p(s(x)))
   fact#(s(x)) -> *#(s(x),fact(p(s(x))))
   *#(s(x),y) -> *#(x,y)
   *#(s(x),y) -> +#(*(x,y),y)
   +#(x,s(y)) -> +#(x,y)
  TRS:
   p(s(x)) -> x
   fact(0()) -> s(0())
   fact(s(x)) -> *(s(x),fact(p(s(x))))
   *(0(),y) -> 0()
   *(s(x),y) -> +(*(x,y),y)
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
  Open