The Runtime Complexity (full) 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:

not(not(x)) → x
not(or(x, y)) → and(not(x), not(y))
not(and(x, y)) → or(not(x), not(y))
and(x, or(y, z)) → or(and(x, y), and(x, z))
and(or(y, z), x) → or(and(x, y), and(x, z))

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
not(or(x, y)) →⁺ and(not(x), not(y))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
The pumping substitution is [x / or(x, y)].
The result substitution is [ ].

(2) BOUNDS(n^1, INF)