(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
incr(nil) → nil
incr(cons(X, L)) → cons(s(X), n__incr(activate(L)))
adx(nil) → nil
adx(cons(X, L)) → incr(cons(X, n__adx(activate(L))))
nats → adx(zeros)
zeros → cons(0, n__zeros)
head(cons(X, L)) → X
tail(cons(X, L)) → activate(L)
incr(X) → n__incr(X)
adx(X) → n__adx(X)
zeros → n__zeros
activate(n__incr(X)) → incr(X)
activate(n__adx(X)) → adx(X)
activate(n__zeros) → zeros
activate(X) → X
Rewrite Strategy: FULL
(1) InfiniteLowerBoundProof (EQUIVALENT transformation)
The loop following loop proves infinite runtime complexity:
The rewrite sequence
incr(cons(X, n__adx(cons(X133_1, n__zeros)))) →+ cons(s(X), n__incr(incr(cons(X133_1, n__adx(cons(0, n__zeros))))))
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 [X / X133_1, X133_1 / 0].
(2) BOUNDS(INF, INF)