A heuristic in the algorithm is consistent if the cost from the current node to a successor node, plus the estimated cost from the successor node to the goal is less than or equal to the estimated cost from the current node to the goal.
In an equation, it would look like this: C(n, n’) + h(n’) ≤ h(n)
A heuristic function is admissible if the estimated cost is never more than the actual cost from the current node to the goal node.
If you want inconsistency and since h(C) <= 3 for the admissibility condition then you should have that h(A) > 1 + h(C). So any heristics that satisfies:
h(A) > 1 + h(C)
h(C) <= 3
h(G) = 0
is admissible and not consistent. You gave
h(A) = 4
h(C) = 1
h(G) = 0
which is a valid candidate.
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