(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
implies(not(x), y) → or(x, y)
implies(not(x), or(y, z)) → implies(y, or(x, z))
implies(x, or(y, z)) → or(y, implies(x, z))
Rewrite Strategy: FULL
(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:
implies(not(x), y) → or(x, y)
implies(not(x), or(y, z)) → implies(y, or(x, z))
implies(x, or(y, z)) → or(y, implies(x, z))
S is empty.
Rewrite Strategy: FULL
(3) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
implies(not(x), or(not(x19_0), z)) →+ implies(x, or(x19_0, z))
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [x / not(x), x19_0 / not(x19_0)].
The result substitution is [ ].
(4) BOUNDS(n^1, INF)