Input TRS:
    1: f(0()) -> cons(0(),n__f(n__s(n__0())))
    2: f(s(0())) -> f(p(s(0())))
    3: p(s(X)) -> X
    4: f(X) -> n__f(X)
    5: s(X) -> n__s(X)
    6: 0() -> n__0()
    7: activate(n__f(X)) -> f(activate(X))
    8: activate(n__s(X)) -> s(activate(X))
    9: activate(n__0()) -> 0()
    10: activate(X) -> X
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3 5 10 7 9
     s(x1)	weight: (/ 3 32) + x1
activate(x1)	weight: (/ 1 32) + 2 * x1
     f(x1)	weight: (/ 7 32) + x1
  n__s(x1)	weight: (/ 1 16) + x1
     p(x1)	weight: x1
     0()	weight: 0
  n__f(x1)	weight: (/ 1 8) + x1
  n__0()	weight: 0
  cons(x1,x2)	weight: x1 + x2
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing f
2: f❆1_s(0()) -> f❆1_p(s(0()))
6: 0() -> n__0()
11: f(p(_1)) ->= f❆1_p(_1)
12: f(s(_1)) ->= f❆1_s(_1)
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 12 11 2
f❆1_p(x1)	weight: 2 * x1
     s(x1)	weight: (/ 153 4) + x1
activate(x1)	weight: x1
f❆1_s(x1)	weight: (/ 307 4) + x1
     f(x1)	weight: (/ 1 2) + 2 * x1
  n__s(x1)	weight: x1
     p(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
  n__f(x1)	weight: x1
  n__0()	weight: 0
  cons(x1,x2)	weight: x1 + x2
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
Number of SCCs: 0, DPs: 0, edges: 0
YES