(0) Obligation:

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

natscons(0, n__incr(nats))
pairscons(0, n__incr(odds))
incr(cons(X, XS)) → cons(s(X), n__incr(activate(XS)))
head(cons(X, XS)) → X
tail(cons(X, XS)) → activate(XS)
incr(X) → n__incr(X)
activate(n__incr(X)) → incr(X)
activate(X) → X

Rewrite Strategy: FULL

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

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