The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(2^n, INF).

(0) Obligation:

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

purge(nil) → nil
purge(.(x, y)) → .(x, purge(remove(x, y)))
remove(x, nil) → nil
remove(x, .(y, z)) → if(=(x, y), remove(x, z), .(y, remove(x, z)))

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(2ⁿ):
The rewrite sequence
remove(x, .(y, z)) →⁺ if(=(x, y), remove(x, z), .(y, remove(x, z)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [z / .(y, z)].
The result substitution is [ ].

The rewrite sequence
remove(x, .(y, z)) →⁺ if(=(x, y), remove(x, z), .(y, remove(x, z)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [2,1].
The pumping substitution is [z / .(y, z)].
The result substitution is [ ].

(2) BOUNDS(2^n, INF)