Runtime Complexity TRS:
The TRS R consists of the following rules:

from(X) → cons(X, n__from(n__s(X)))
after(0, XS) → XS
after(s(N), cons(X, XS)) → after(N, activate(XS))
from(X) → n__from(X)
s(X) → n__s(X)
activate(n__from(X)) → from(activate(X))
activate(n__s(X)) → s(activate(X))
activate(X) → X

Rewrite Strategy: INNERMOST

Renamed function symbols to avoid clashes with predefined symbol.

Runtime Complexity TRS:
The TRS R consists of the following rules:

from'(X) → cons'(X, n__from'(n__s'(X)))
after'(0', XS) → XS
after'(s'(N), cons'(X, XS)) → after'(N, activate'(XS))
from'(X) → n__from'(X)
s'(X) → n__s'(X)
activate'(n__from'(X)) → from'(activate'(X))
activate'(n__s'(X)) → s'(activate'(X))
activate'(X) → X

Rewrite Strategy: INNERMOST

Sliced the following arguments:
cons'/0

Runtime Complexity TRS:
The TRS R consists of the following rules:

from'(X) → cons'(n__from'(n__s'(X)))
after'(0', XS) → XS
after'(s'(N), cons'(XS)) → after'(N, activate'(XS))
from'(X) → n__from'(X)
s'(X) → n__s'(X)
activate'(n__from'(X)) → from'(activate'(X))
activate'(n__s'(X)) → s'(activate'(X))
activate'(X) → X

Rewrite Strategy: INNERMOST

Infered types.

Rules:
from'(X) → cons'(n__from'(n__s'(X)))
after'(0', XS) → XS
after'(s'(N), cons'(XS)) → after'(N, activate'(XS))
from'(X) → n__from'(X)
s'(X) → n__s'(X)
activate'(n__from'(X)) → from'(activate'(X))
activate'(n__s'(X)) → s'(activate'(X))
activate'(X) → X

Types:
from' :: n__s':n__from':cons':0' → n__s':n__from':cons':0'
cons' :: n__s':n__from':cons':0' → n__s':n__from':cons':0'
n__from' :: n__s':n__from':cons':0' → n__s':n__from':cons':0'
n__s' :: n__s':n__from':cons':0' → n__s':n__from':cons':0'
after' :: n__s':n__from':cons':0' → n__s':n__from':cons':0' → n__s':n__from':cons':0'
0' :: n__s':n__from':cons':0'
s' :: n__s':n__from':cons':0' → n__s':n__from':cons':0'
activate' :: n__s':n__from':cons':0' → n__s':n__from':cons':0'
_hole_n__s':n__from':cons':0'1 :: n__s':n__from':cons':0'
_gen_n__s':n__from':cons':0'2 :: Nat → n__s':n__from':cons':0'

Heuristically decided to analyse the following defined symbols:
after', activate'

They will be analysed ascendingly in the following order:
activate' < after'

Generator Equations:
_gen_n__s':n__from':cons':0'2(0) ⇔ 0'
_gen_n__s':n__from':cons':0'2(+(x, 1)) ⇔ cons'(_gen_n__s':n__from':cons':0'2(x))

The following defined symbols remain to be analysed:
activate', after'

They will be analysed ascendingly in the following order:
activate' < after'

Could not prove a rewrite lemma for the defined symbol activate'.

Generator Equations:
_gen_n__s':n__from':cons':0'2(0) ⇔ 0'
_gen_n__s':n__from':cons':0'2(+(x, 1)) ⇔ cons'(_gen_n__s':n__from':cons':0'2(x))

The following defined symbols remain to be analysed:
after'

Could not prove a rewrite lemma for the defined symbol after'.

Generator Equations:
_gen_n__s':n__from':cons':0'2(0) ⇔ 0'
_gen_n__s':n__from':cons':0'2(+(x, 1)) ⇔ cons'(_gen_n__s':n__from':cons':0'2(x))

No more defined symbols left to analyse.