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:

f(c(X, s(Y))) → f(c(s(X), Y))
g(c(s(X), Y)) → f(c(X, s(Y)))

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 2.

The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by:
final states : [1, 2]
transitions:
c0(0, 0) → 0
s0(0) → 0
f0(0) → 1
g0(0) → 2
s1(0) → 4
c1(4, 0) → 3
f1(3) → 1
s1(0) → 6
c1(0, 6) → 5
f1(5) → 2
s1(4) → 4
s2(0) → 8
c2(8, 0) → 7
f2(7) → 2
s1(8) → 4
f1(3) → 2

(2) BOUNDS(1, n^1)