(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
not(and(x, y)) → or(not(x), not(y))
not(or(x, y)) → and(not(x), not(y))
and(x, or(y, z)) → or(and(x, y), and(x, z))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCpxRelTrsProof (BOTH BOUNDS(ID, ID) transformation)
Transformed TRS to relative TRS where S is empty.
(2) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
not(and(x, y)) → or(not(x), not(y))
not(or(x, y)) → and(not(x), not(y))
and(x, or(y, z)) → or(and(x, y), and(x, z))
S is empty.
Rewrite Strategy: INNERMOST
(3) 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 [ ].
(4) BOUNDS(n^1, INF)