(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
from(X) → cons(X, from(s(X)))
head(cons(X, XS)) → X
2nd(cons(X, XS)) → head(XS)
take(0, XS) → nil
take(s(N), cons(X, XS)) → cons(X, take(N, XS))
sel(0, cons(X, XS)) → X
sel(s(N), cons(X, XS)) → sel(N, XS)
Rewrite Strategy: INNERMOST
(1) InfiniteLowerBoundProof (EQUIVALENT transformation)
The loop following loop proves infinite runtime complexity:
The rewrite sequence
from(X) →+ cons(X, from(s(X)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [ ].
The result substitution is [X / s(X)].
(2) BOUNDS(INF, INF)