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

(0) Obligation:

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

admit(x, nil) → nil
admit(x, .(u, .(v, .(w, z)))) → cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z)))))
cond(true, y) → y

Rewrite Strategy: INNERMOST

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
admit(x, .(u, .(v, .(w, z)))) →⁺ cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z)))))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1,1,1,1].
The pumping substitution is [z / .(u, .(v, .(w, z)))].
The result substitution is [x / carry(x, u, v)].

(2) BOUNDS(n^1, INF)