MAYBE

Problem:
 plus(x,0()) -> x
 plus(x,s(y)) -> s(plus(x,y))
 times(0(),y) -> 0()
 times(x,0()) -> 0()
 times(s(x),y) -> plus(times(x,y),y)
 p(s(s(x))) -> s(p(s(x)))
 p(s(0())) -> 0()
 fac(s(x)) -> times(fac(p(s(x))),s(x))

Proof:
 DP Processor:
  DPs:
   plus#(x,s(y)) -> plus#(x,y)
   times#(s(x),y) -> times#(x,y)
   times#(s(x),y) -> plus#(times(x,y),y)
   p#(s(s(x))) -> p#(s(x))
   fac#(s(x)) -> p#(s(x))
   fac#(s(x)) -> fac#(p(s(x)))
   fac#(s(x)) -> times#(fac(p(s(x))),s(x))
  TRS:
   plus(x,0()) -> x
   plus(x,s(y)) -> s(plus(x,y))
   times(0(),y) -> 0()
   times(x,0()) -> 0()
   times(s(x),y) -> plus(times(x,y),y)
   p(s(s(x))) -> s(p(s(x)))
   p(s(0())) -> 0()
   fac(s(x)) -> times(fac(p(s(x))),s(x))
  Open