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MiniZinc

include "all_different.mzn";
predicate fzn_circuit(array[int] of var int: x) =
let { set of int: S = index_set(x),
int: l = min(S),
int: n = card(S),
array[S] of var 1..n: order
} in
all_different(x) /\
all_different(order) /\
forall(i in S)(x[i] != i) /\
order[l] = 1 /\
forall(i in S)(order[i] != n -> order[x[i]] = order[i] + 1) /\
forall(i in S)(order[i] == n -> x[i] = l );
%-----------------------------------------------------------------------------%