Input TRS:
    1: fac(s(x)) -> *(fac(p(s(x))),s(x))
    2: p(s(0())) -> 0()
    3: p(s(s(x))) -> s(p(s(x)))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing p
1: fac(s(x)) -> *(fac(p❆1_s(x)),s(x))
2: p❆1_s(0()) -> 0()
3: p❆1_s(s(x)) -> s(p❆1_s(x))
4: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 4 1
     s(x1)	weight: (/ 1 4) + 2 * x1
p❆1_s(x1)	weight: x1
     p(x1)	weight: 2 * x1
     0()	weight: 0
   fac(x1)	weight: (/ 211469 4) + 2 * x1
     *(x1,x2)	weight: x1 + x2
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 3 2
     s(x1)	weight: (/ 3 4) + 2 * x1
p❆1_s(x1)	weight: (/ 1 4) + 2 * x1
     p(x1)	weight: 2 * x1
     0()	weight: 0
   fac(x1)	weight: (/ 211469 4) + 2 * x1
     *(x1,x2)	weight: x1 + x2
Number of strict rules: 0
YES