Task environment:

Performance measure: The target jug(4-gallon) is filled with the given amount (2 gallon) or not
Environment of Agent: The two jugs (4-gallon and 2-gallon jug) and water level in each jug are the environment of agent.
Actuators: The actions that can be taken according to the production rules are the actuators.
Sensors: The program which maintains the water level in each jug (state) are the sensors.

Production Rules:

(specific to case 3 gallon and 4 gallon jug water)

(x,y / x<4) -> (4,y)-------Fill the 4-gallon jug.
(x,y / y<3) -> (x,3)------Fill the 3-gallon jug
(x,y / x>0) -> (x-d,y)-----Pour some water out of the 4-gallon jug
(x,y / y>0) -> (x,y-d)------Pour some water out of the 3-gallon jug
(x,y / y>0) -> (x,0)------Empty the 3-gallon jug on ground.
(x,y / x+y>=4 ^ y>0) -> (4,y-(4-x)) ------our water from 3-gallon jug to the 4-gallon jug until the 4-gallon jug is full.
(x,y | x+y>=3 ^ x>0) -> (x-(3-y),3) ------ Pour water from 4-gallon jug into 3-gallon jug until 3-gallon jug is full.
(x,y | x+y<=4 ^ y>0) -> (x+y,0) ------ Pour all water from 3-gallon jug into 4-gallon jug.
(x,y | x+y <=3 ^ x>0) -> (0,x+y) ------ Pour all water from 4-gallon jug into 3-gallon jug.
(0,2) -> (2,0) ------ Pour 2 gallon water from 3 gallon jug into 4 gallon jug.