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) CpxTrsToCpxRelTrsProof (BOTH BOUNDS(ID, ID) transformation)

Transformed TRS to relative TRS where S is empty.

(2) Obligation:

Runtime Complexity Relative 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)

S is empty.
Rewrite Strategy: INNERMOST

(3) SlicingProof (LOWER BOUND(ID) transformation)

Sliced the following arguments:
Cons/0

(4) Obligation:

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

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

S is empty.
Rewrite Strategy: INNERMOST

(5) InfiniteLowerBoundProof (EQUIVALENT transformation)

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

(6) BOUNDS(INF, INF)