(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
nats → adx(zeros)
zeros → cons(0, zeros)
incr(cons(X, Y)) → cons(s(X), incr(Y))
adx(cons(X, Y)) → incr(cons(X, adx(Y)))
hd(cons(X, Y)) → X
tl(cons(X, Y)) → Y
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 [ ].
(2) BOUNDS(INF, INF)