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:

minus(minus(x)) → x
minus(h(x)) → h(minus(x))
minus(f(x, y)) → f(minus(y), minus(x))

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]
transitions:
h0(0) → 0
f0(0, 0) → 0
minus0(0) → 1
minus1(0) → 2
h1(2) → 1
minus1(0) → 3
minus1(0) → 4
f1(3, 4) → 1
h1(2) → 2
h1(2) → 3
h1(2) → 4
f1(3, 4) → 2
f1(3, 4) → 3
f1(3, 4) → 4

(2) BOUNDS(1, n^1)