The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).

(0) Obligation:

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

addlist(Cons(x, xs'), Cons(S(0), xs)) → Cons(S(x), addlist(xs', xs))
addlist(Cons(S(0), xs'), Cons(x, xs)) → Cons(S(x), addlist(xs', xs))
addlist(Nil, ys) → Nil
notEmpty(Cons(x, xs)) → True
notEmpty(Nil) → False
goal(xs, ys) → addlist(xs, ys)

Rewrite Strategy: INNERMOST

(1) CpxTrsMatchBoundsTAProof (EQUIVALENT transformation)

A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 1.

The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by:
final states : [1, 2, 3]
transitions:
Cons0(0, 0) → 0
S0(0) → 0
00() → 0
Nil0() → 0
True0() → 0
False0() → 0
addlist0(0, 0) → 1
notEmpty0(0) → 2
goal0(0, 0) → 3
S1(0) → 4
addlist1(0, 0) → 5
Cons1(4, 5) → 1
Nil1() → 1
True1() → 2
False1() → 2
addlist1(0, 0) → 3
Cons1(4, 5) → 3
Cons1(4, 5) → 5
Nil1() → 3
Nil1() → 5

(2) BOUNDS(1, n^1)