(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
and(tt, X) → activate(X)
plus(N, 0) → N
plus(N, s(M)) → s(plus(N, M))
activate(X) → X
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:
and(tt, X) → activate(X)
plus(N, 0) → N
plus(N, s(M)) → s(plus(N, M))
activate(X) → X
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
plus(N, s(M)) →+ s(plus(N, M))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
The pumping substitution is [M / s(M)].
The result substitution is [ ].
(4) BOUNDS(n^1, INF)