The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

badd(x', Cons(x, xs)) → badd(Cons(Nil, Nil), badd(x', xs))
badd(x, Nil) → x
goal(x, y) → badd(x, y)

Rewrite Strategy: INNERMOST

(1) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
badd(Cons(x86_0, Nil), Cons(x, Nil)) →⁺ badd(Cons(Nil, Nil), Cons(Nil, Nil))
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [ ].
The result substitution is [x86_0 / Nil, x / Nil].

(2) BOUNDS(INF, INF)