Input TRS:
    1: f(0()) -> cons(0(),n__f(s(0())))
    2: f(s(0())) -> f(p(s(0())))
    3: p(s(X)) -> X
    4: f(X) -> n__f(X)
    5: activate(n__f(X)) -> f(X)
    6: activate(X) -> X
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... removes: 4 1 3 5 6
     s(x1)	weight: (/ 1 8) + x1
activate(x1)	weight: (/ 1 4) + 2 * x1
     f(x1)	weight: (/ 3 8) + x1
     p(x1)	weight: x1
     0()	weight: 0
  n__f(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: x1 + x2
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
2: f❆1_s(0()) -> f❆1_p(s(0()))
7: f(p(_1)) ->= f❆1_p(_1)
8: f(s(_1)) ->= f❆1_s(_1)
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... removes: 8 7 2
f❆1_p(x1)	weight: 2 * x1
     s(x1)	weight: (/ 1 4) + x1
activate(x1)	weight: x1
f❆1_s(x1)	weight: (/ 3 4) + x1
     f(x1)	weight: (/ 1 2) + 2 * x1
     p(x1)	weight: (/ 30877 4) + x1
     0()	weight: 0
  n__f(x1)	weight: x1
  cons(x1,x2)	weight: x1 + x2
Number of strict rules: 0
YES