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

(0) Obligation:

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

R(2(x1)) → 2(R(x1))
R(3(x1)) → 3(R(x1))
R(1(x1)) → L(3(x1))
3(L(x1)) → L(3(x1))
2(L(x1)) → L(2(x1))
0(L(x1)) → 2(R(x1))
R(b(x1)) → c(1(b(x1)))
3(c(x1)) → c(1(x1))
2(c(1(x1))) → c(0(R(1(x1))))
2(c(0(x1))) → c(0(0(x1)))

Rewrite Strategy: INNERMOST

(1) CpxTrsMatchBoundsProof (EQUIVALENT transformation)

A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 6.
The certificate found is represented by the following graph.

Start state: 2254
Accept states: [2255, 2256, 2257, 2258]
Transitions:
2254→2255[R_1|0]
2254→2256[3_1|0]
2254→2257[2_1|0]
2254→2258[0_1|0]
2254→2254[1_1|0, L_1|0, b_1|0, c_1|0]
2254→2259[3_1|1]
2254→2260[1_1|1]
2254→2263[3_1|1]
2254→2264[2_1|1]
2254→2265[R_1|1]
2254→2266[b_1|1]
2254→2268[1_1|1]
2254→2271[3_1|2]
2254→2277[1_1|2]
2254→2280[R_1|3]
2254→2285[3_1|3]
2254→2294[b_1|2]
2254→2296[R_1|4]
2259→2255[L_1|1]
2259→2265[L_1|1]
2259→2272[2_1|2]
2259→2280[L_1|1]
2259→2287[3_1|2]
2259→2296[L_1|1]
2260→2261[R_1|1]
2261→2262[0_1|1]
2262→2257[c_1|1]
2262→2264[c_1|1]
2263→2256[L_1|1]
2263→2259[L_1|1]
2263→2263[L_1|1]
2263→2271[L_1|1]
2263→2281[2_1|2]
2263→2285[L_1|1]
2263→2297[3_1|2]
2264→2257[L_1|1]
2264→2264[L_1|1]
2265→2258[2_1|1]
2266→2267[1_1|1]
2266→2273[1_1|2]
2266→2282[3_1|3]
2266→2288[R_1|4]
2266→2325[3_1|2]
2267→2255[c_1|1]
2267→2265[c_1|1]
2267→2280[c_1|1]
2267→2289[1_1|2]
2267→2298[1_1|3]
2267→2296[c_1|1]
2267→2306[3_1|4]
2267→2322[R_1|5]
2268→2256[c_1|1]
2268→2259[c_1|1]
2268→2263[c_1|1]
2268→2271[c_1|1]
2268→2285[c_1|1]
2268→2301[1_1|2]
2268→2307[1_1|3]
2268→2314[3_1|4]
2268→2326[R_1|5]
2271→2261[L_1|2]
2271→2276[R_1|2]
2271→2326[L_1|2]
2271→2334[3_1|3]
2272→2258[L_1|2]
2273→2274[R_1|2]
2274→2275[0_1|2]
2275→2258[c_1|2]
2276→2262[2_1|2]
2277→2278[R_1|2]
2278→2279[0_1|2]
2279→2272[c_1|2]
2279→2281[c_1|2]
2280→2276[3_1|3]
2281→2272[L_1|2]
2281→2281[L_1|2]
2282→2274[L_1|3]
2282→2286[R_1|3]
2285→2278[L_1|3]
2285→2290[R_1|3]
2286→2275[2_1|3]
2287→2276[L_1|2]
2287→2302[2_1|3]
2287→2290[L_1|2]
2288→2286[3_1|4]
2289→2276[c_1|2]
2289→2290[c_1|2]
2290→2279[2_1|3]
2294→2295[1_1|2]
2294→2335[3_1|3]
2295→2288[c_1|2]
2295→2310[1_1|3]
2295→2315[1_1|4]
2295→2323[3_1|5]
2295→2330[R_1|6]
2296→2290[3_1|4]
2297→2287[L_1|2]
2297→2297[L_1|2]
2297→2311[2_1|3]
2297→2334[L_1|2]
2298→2299[R_1|3]
2299→2300[0_1|3]
2300→2262[c_1|3]
2300→2279[c_1|3]
2301→2287[c_1|2]
2301→2297[c_1|2]
2301→2334[c_1|2]
2302→2262[L_1|3]
2302→2279[L_1|3]
2306→2299[L_1|4]
2306→2318[R_1|4]
2307→2308[R_1|3]
2308→2309[0_1|3]
2309→2302[c_1|3]
2309→2311[c_1|3]
2309→2337[c_1|3]
2310→2286[c_1|3]
2311→2302[L_1|3]
2311→2311[L_1|3]
2311→2337[L_1|3]
2314→2308[L_1|4]
2314→2324[R_1|4]
2315→2316[R_1|4]
2316→2317[0_1|4]
2317→2275[c_1|4]
2318→2300[2_1|4]
2322→2318[3_1|5]
2323→2316[L_1|5]
2323→2327[R_1|5]
2324→2309[2_1|4]
2325→2322[L_1|2]
2325→2331[3_1|3]
2326→2324[3_1|5]
2327→2317[2_1|5]
2330→2327[3_1|6]
2331→2318[L_1|3]
2331→2336[2_1|4]
2334→2324[L_1|3]
2334→2337[2_1|4]
2335→2330[L_1|3]
2335→2338[3_1|4]
2336→2300[L_1|4]
2337→2309[L_1|4]
2338→2327[L_1|4]
2338→2343[2_1|5]
2343→2317[L_1|5]

(2) BOUNDS(O(1), O(n^1))