Input TRS:
    1: f(0()) -> s(0())
    2: f(s(0())) -> s(s(0()))
    3: f(s(0())) -> *(s(s(0())),f(0()))
    4: f(+(x,s(0()))) -> +(s(s(0())),f(x))
    5: f(+(x,y)) -> *(f(x),f(y))
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... removes: 1 5 2
     s(x1)	weight: x1
     f(x1)	weight: (/ 1 8) + x1
     0()	weight: 0
     +(x1,x2)	weight: (/ 1 4) + x1 + x2
     *(x1,x2)	weight: x1 + x2
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 4
     s(x1)	weight: x1
     f(x1)	weight: (/ 1 4) + 2 * x1
     0()	weight: 0
     +(x1,x2)	weight: (/ 122449 4) + x1 + x2
     *(x1,x2)	weight: x1 + x2
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
3: f❆1_s(0()) -> *(s(s(0())),f❆1_0())
6: f(0()) ->= f❆1_0()
7: f(s(_1)) ->= f❆1_s(_1)
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... removes: 3 7 6
     s(x1)	weight: (/ 1 8) + x1
f❆1_s(x1)	weight: (/ 3 8) + x1
     f(x1)	weight: (/ 1 4) + 2 * x1
     0()	weight: 0
     +(x1,x2)	weight: x1 + x2
f❆1_0()	weight: 0
     *(x1,x2)	weight: x1 + x2
Number of strict rules: 0
YES