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This paper is a continuation of  and concerns if-while algebras over integers. In these algebras the only elementary instructions are assignment instructions. The instruction assigns to a (program) variable a value which is calculated for the current state according to some arithmetic expression. The expression may include variables, constants, and a limited number of arithmetic operations. States are functions from a given set of locations into integers. A variable is a function from thedoi:10.2478/v10037-008-0024-0 fatcat:ztgamxlt2baa7mrdrckifwkipa