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This watchdog mode will obviously slow down the specialisation process, invalidating one of the advantages of the oﬄine approach. , apparent non-termination) arises: it is not our intention to have the watchdog mode permanently enabled (in that case an online partial evaluator would be more appropriate). In this paper we formally develop this idea, present an implementation inside the logen system  and evaluate its performance on a series of examples. We show that on most correct annotations no false alarms are raised, while on incorrect annotations the problems are spotted quickly and useful feedback is given.
2. Q and R are contradictory iff both P1 and P2 are contradictory. 3. Q and R are incoherent iff either P1 or P2 is incoherent. 2. When two programs P1 and P2 are both categorical, minimal and maximal consensus coincide. 1, when one of two programs is inconsistent, the results of consensus are rather trivial. We thus consider consensus of consistent programs hereafter. 3. Let P1 and P2 be two consistent programs, Q a minimal consensus, and R a maximal consensus. Then, 1. ∀U ∈ AS(Q), ∃S ∈ AS(P1 ) and ∃T ∈ AS(P2 ) such that U ⊆ S and U ⊆ T .
Craig, and D. Elphick A widely used wqo is the homeomorphic embedding relation ✂. , [14, 15] for a summary of its use in online control). In what follows, we deﬁne an expression to be either a term, an atom, a conjunction, or a goal. Deﬁnition 2. e. ✂ is the least relation satisfying the rules): 1. X ✂ Y for all variables X, Y 2. s ✂ f (t1 , . .