(0) Obligation:

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

incr(nil) → nil
incr(cons(X, L)) → cons(s(X), incr(L))
adx(nil) → nil
adx(cons(X, L)) → incr(cons(X, adx(L)))
zeroscons(0, zeros)
head(cons(X, L)) → X
tail(cons(X, L)) → L

Rewrite Strategy: FULL

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
zeros →+ cons(0, zeros)
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [ ].
The result substitution is [ ].