(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
and(true, X) → X
and(false, Y) → false
if(true, X, Y) → X
if(false, X, Y) → Y
add(0, X) → X
add(s(X), Y) → s(add(X, Y))
first(0, X) → nil
first(s(X), cons(Y, Z)) → cons(Y, first(X, Z))
from(X) → cons(X, from(s(X)))
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)