(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
fst(0, Z) → nil
fst(s(X), cons(Y, Z)) → cons(Y, n__fst(activate(X), activate(Z)))
from(X) → cons(X, n__from(s(X)))
add(0, X) → X
add(s(X), Y) → s(n__add(activate(X), Y))
len(nil) → 0
len(cons(X, Z)) → s(n__len(activate(Z)))
fst(X1, X2) → n__fst(X1, X2)
from(X) → n__from(X)
add(X1, X2) → n__add(X1, X2)
len(X) → n__len(X)
activate(n__fst(X1, X2)) → fst(X1, X2)
activate(n__from(X)) → from(X)
activate(n__add(X1, X2)) → add(X1, X2)
activate(n__len(X)) → len(X)
activate(X) → X
Rewrite Strategy: INNERMOST
(1) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
add(s(n__add(X13562_3, X23563_3)), Y) →+ s(n__add(add(X13562_3, X23563_3), Y))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
The pumping substitution is [X13562_3 / s(n__add(X13562_3, X23563_3))].
The result substitution is [Y / X23563_3].
(2) BOUNDS(n^1, INF)