Initial state: (0, 0) means both jugs are empty.

% Goal state: (2, _), where the first jug has exactly 2 liters of water.


% The capacity of the jugs

capacity(4, 3).


% Define possible actions: fill, empty, pour from one jug to another.


% Fill the 4-liter jug

action((X, Y), (4, Y)) :-

    capacity(4, _),

    X < 4.


% Fill the 3-liter jug

action((X, Y), (X, 3)) :-

    capacity(_, 3),

    Y < 3.


% Empty the 4-liter jug

action((X, Y), (0, Y)) :-

    X > 0.


% Empty the 3-liter jug

action((X, Y), (X, 0)) :-

    Y > 0.


% Pour water from the 4-liter jug into the 3-liter jug

action((X, Y), (NewX, NewY)) :-

    capacity(_, MaxY),

    X > 0,

    Y < MaxY,

    Transfer is min(X, MaxY - Y),

    NewX is X - Transfer,

    NewY is Y + Transfer.


% Pour water from the 3-liter jug into the 4-liter jug

action((X, Y), (NewX, NewY)) :-

    capacity(MaxX, _),

    Y > 0,

    X < MaxX,

    Transfer is min(Y, MaxX - X),

    NewY is Y - Transfer,

    NewX is X + Transfer.


% Define the search predicate to reach the goal state (2, _)

solve(Path) :-

    search((0, 0), [(0, 0)], Path).


% Recursive search to find the solution path

search((2, _), Visited, Path) :-

    reverse(Visited, Path).


search(State, Visited, Path) :-

    action(State, NextState),

    \+ member(NextState, Visited), % Avoid revisiting states

    search(NextState, [NextState | Visited], Path).

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