#### Pitfalls of Interval Reasoning

In most circumstances, arithmetic constraints maintain
interval-consistency and detect interval-entailment and
-disentailment. There are cases where an interval-consistency
maintaining constraint may detect a contradiction when the constraint is
not yet interval-disentailed, as the following example illustrates.
Note that

`X`` #\= `

`Y`

maintains domain-consistency if
both arguments are constants or variables:

| ?- `X+Y #= Z, X=1, Z=6, Y in 1..10, Y #\= 5.`
no
| ?- `X+Y #= Z #<=> B, X=1, Z=6, Y in 1..10, Y #\= 5.`
X = 1,
Z = 6,
Y in(1..4)\/(6..10),
B in 0..1

Since `1+5#=6`

holds, `X+Y #= Z`

is not interval-disentailed,
although any attempt to make it interval-consistent wrt. the store
results in a contradictory store.