[30 50]{R9 R3 R1 W12 W1 W0}, [200 205]{R10 R2 R4 W12 W1 W0}} ⊕lc {[20 40]{R0 W1}}=
{[20 40]{R3 R1 R0 W1 W0}, [20 25]{R0 R3 R1 W11 W1 W0}, [30 40]{R9 R3 R1 R0 W12 W1 W0}} ≠ ∅
Thus, the new constraint (n1 {[20 40]} n2) is consistent in context W1. Therefore, the constraint between n1 n2 results:
lc12 ← (lc12 - get (n1, n2, W1)) ∪lc (lc12 ⊕lc {[20 40]{R0 W1}}) =
{[0 100]{R1 W0}, [200 300]{R2 W0}, [60 100]{R5 R1 W2 W0}, [290 300]{R6 R2 W2 W0},
[0 25]{R7 R1 W3 W0}, [260 280]{R8 R2 W3 W0}, [0 20]{R0 R7 R1 W31 W3 W0},
[210 215]{R0 R2 R8 W32 W3 W0}, [260 280]{R0 R2 R8 W33 W3 W0}} ∪lc
{[20 40]{R1 R0 W1 W0}, [20 40]{R3 R1 R0 W1 W0}, [20 25]{R0 R3 R1 W11 W1 W0}, [30 40]{R9 R3 R1 R0 W12 W1 W0}}=
{[0 100]{R1 W0}, [200 300]{R2 W0}, [60 100]{R5 R1 W2 W0}, [290 300]{R6 R2 W2 W0}, [0 25]{R7 R1 W3 W0}, (e4)
 [260 280]{R8 R2 W3 W0}, [0 20]{R0 R7 R1 W31 W3 W0}, [210 215]{R0 R2 R8 W32 W3 W0}, [260 280]{R0 R2 R8 W33 W3 W0},
[20 40]{R1 R0 W1 W0}, [20 25]{R0 R3 R1 W11 W1 W0}, [30 40]{R9 R3 R1 R0 W12 W1 W0}}.

Note that the new updated constraint is asserted in context W1 and propagated to all its successor contexts (W11 and W12). However, the new constraint in context W1 does not affect the existing constraints in predecessor contexts of W1 (W0) nor the constraints belonging to contexts of different hierarchies (W2, W3 and their successors).

In this update process, no closure process is performed, since no node is related with n1 or n2.

Now, let's update (n3 {[10 20]} n1) in context W1. We have:
Consistency-Test (get-upward (n3, n1, W1), {[10 20]{R0 W1}}),
that performs:
{(-∞ +∞)}{W0 R0} ⊕lc {[20 40]{R0 W1}} = {[20 40]{R0 W0 W1}} ≠ ∅,
since no previous constraint exists between (n3 n1) in context W1. The constraint (n3 {[10 20]} n1) is consistent, and asserted in the TCN:
lc31 ← {(-∞ +∞)}{W0 R0}, [20 40]{R0 W0 W1}}. (e5)
Afterwards, this constraint is closured. The call to Context-Closure process is:
Context-Closure (n3, {(-∞ +∞)}{W0 R0}, [20 40]{R0 W0 W1}}, n1, W1).

In this closure process, only the first loop is performed since no node is related to n3. Moreover, only the previous constraint lc12 (expression e4) exists in the current TCN between n1 and n2. Thus, the first loop performs:
lc'32 ← lc32 ⊕lc ({(-∞ +∞)}{W0 R0}, [20 40]{R0 W0 W1}} ⊗lc lc12) =
{(-∞ ∞){W0 R0}} ⊕lc ({(-∞ +∞)}{W0 R0}, [20 40]{R0 W0 W1}} ⊗lc lc12) = {(-∞ +∞)}{W0 R0}, [220 340]{R2 R0 W0 W1}, [40 80]{R1 R0 W1 W0},
[40 65]{R0 R3 R1 W11 W1 W0}, [50 80]{R9 R3 R1 R0 W12 W1 W0}},
such that, lc32 ← (lc32 - get (n3, n2, W1)) ∪lc lc'32 = ({(-∞ ∞){W0 R0}} - {}) ∪lc lc'32 =
{(-∞ ∞){W0 R0}, [220 340]{R2 R0 W0 W1}, [40 80]{R1 R0 W1 W0}, 
[40 65]{R0 R3 R1 W11 W1 W0}, [50 80]{R9 R3 R1 R0 W12 W1 W0}}. (e6)