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

a__from(X) → cons(mark(X), from(s(X)))
a__after(0, XS) → mark(XS)
a__after(s(N), cons(X, XS)) → a__after(mark(N), mark(XS))
mark(from(X)) → a__from(mark(X))
mark(after(X1, X2)) → a__after(mark(X1), mark(X2))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))
mark(0) → 0
a__from(X) → from(X)
a__after(X1, X2) → after(X1, X2)

Rewrite Strategy: INNERMOST

Renamed function symbols to avoid clashes with predefined symbol.

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

a__from'(X) → cons'(mark'(X), from'(s'(X)))
a__after'(0', XS) → mark'(XS)
a__after'(s'(N), cons'(X, XS)) → a__after'(mark'(N), mark'(XS))
mark'(from'(X)) → a__from'(mark'(X))
mark'(after'(X1, X2)) → a__after'(mark'(X1), mark'(X2))
mark'(cons'(X1, X2)) → cons'(mark'(X1), X2)
mark'(s'(X)) → s'(mark'(X))
mark'(0') → 0'
a__from'(X) → from'(X)
a__after'(X1, X2) → after'(X1, X2)

Rewrite Strategy: INNERMOST

Infered types.

Rules:
a__from'(X) → cons'(mark'(X), from'(s'(X)))
a__after'(0', XS) → mark'(XS)
a__after'(s'(N), cons'(X, XS)) → a__after'(mark'(N), mark'(XS))
mark'(from'(X)) → a__from'(mark'(X))
mark'(after'(X1, X2)) → a__after'(mark'(X1), mark'(X2))
mark'(cons'(X1, X2)) → cons'(mark'(X1), X2)
mark'(s'(X)) → s'(mark'(X))
mark'(0') → 0'
a__from'(X) → from'(X)
a__after'(X1, X2) → after'(X1, X2)

Types:
a__from' :: s':from':cons':0':after' → s':from':cons':0':after'
cons' :: s':from':cons':0':after' → s':from':cons':0':after' → s':from':cons':0':after'
mark' :: s':from':cons':0':after' → s':from':cons':0':after'
from' :: s':from':cons':0':after' → s':from':cons':0':after'
s' :: s':from':cons':0':after' → s':from':cons':0':after'
a__after' :: s':from':cons':0':after' → s':from':cons':0':after' → s':from':cons':0':after'
0' :: s':from':cons':0':after'
after' :: s':from':cons':0':after' → s':from':cons':0':after' → s':from':cons':0':after'
_hole_s':from':cons':0':after'1 :: s':from':cons':0':after'
_gen_s':from':cons':0':after'2 :: Nat → s':from':cons':0':after'

Heuristically decided to analyse the following defined symbols:
a__from', mark', a__after'

They will be analysed ascendingly in the following order:
a__from' = mark'
a__from' = a__after'
mark' = a__after'

Generator Equations:
_gen_s':from':cons':0':after'2(0) ⇔ 0'
_gen_s':from':cons':0':after'2(+(x, 1)) ⇔ cons'(0', _gen_s':from':cons':0':after'2(x))

The following defined symbols remain to be analysed:
mark', a__from', a__after'

They will be analysed ascendingly in the following order:
a__from' = mark'
a__from' = a__after'
mark' = a__after'

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

Generator Equations:
_gen_s':from':cons':0':after'2(0) ⇔ 0'
_gen_s':from':cons':0':after'2(+(x, 1)) ⇔ cons'(0', _gen_s':from':cons':0':after'2(x))

The following defined symbols remain to be analysed:
a__from', a__after'

They will be analysed ascendingly in the following order:
a__from' = mark'
a__from' = a__after'
mark' = a__after'

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

Generator Equations:
_gen_s':from':cons':0':after'2(0) ⇔ 0'
_gen_s':from':cons':0':after'2(+(x, 1)) ⇔ cons'(0', _gen_s':from':cons':0':after'2(x))

The following defined symbols remain to be analysed:
a__after'

They will be analysed ascendingly in the following order:
a__from' = mark'
a__from' = a__after'
mark' = a__after'

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

Generator Equations:
_gen_s':from':cons':0':after'2(0) ⇔ 0'
_gen_s':from':cons':0':after'2(+(x, 1)) ⇔ cons'(0', _gen_s':from':cons':0':after'2(x))

No more defined symbols left to analyse.