Input TRS:
    1: p(s(x)) -> x
    2: fac(0()) -> s(0())
    3: fac(s(x)) -> times(s(x),fac(p(s(x))))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing p
1: p❆1_s(x) -> x
2: fac(0()) -> s(0())
3: fac(s(x)) -> times(s(x),fac(p❆1_s(x)))
4: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 4 1 3 2
     s(x1)	weight: (/ 3 4) + 2 * x1
p❆1_s(x1)	weight: (/ 1 4) + x1
     p(x1)	weight: 2 * x1
     0()	weight: 0
 times(x1,x2)	weight: x1 + x2
   fac(x1)	weight: 5854 + 2 * x1
Number of strict rules: 0
YES