include "expr-grammar-ambiguos.Grm"

% Part 2.  Transformation rules
rule main
    replace [expression]
        E [expression]
    construct NewE [expression]
        E [removePlusZero1] [removePlusZero2] [removeMinusZero]
	[removeMultiplicationByOne1] [removeMultiplicationByOne2]
	[removeDivisionByOne] [resolveMultiplicationByZero1]
        [resolveMultiplicationByZero2] [resolveBracket]
        [resolveDouble] [resolveDoubleDivision]
    where not
        NewE [= E]
    by
        NewE
end rule

rule removePlusZero1
    replace [expression]
        N1 [expression] + 0
    by
        N1
end rule

rule removePlusZero2
    replace [expression]
         0 + N1 [expression]
    by
        N1
end rule

rule removeMinusZero
    replace [expression]
        N1 [expression] - 0
    by
        N1
end rule

rule removeMultiplicationByOne1
    replace [expression]
        N1 [expression] * 1
    by
        N1
end rule 

rule removeMultiplicationByOne2
    replace [expression]
         1 * N1 [expression]
    by
        N1
end rule

rule resolveMultiplicationByZero1
    replace [expression]
        N1 [expression] * 0
    by
        0
end rule

rule resolveMultiplicationByZero2
    replace [expression]
         0 * N1 [expression]
    by
        0
end rule

rule removeDivisionByOne
    replace [expression]
        N1 [expression] / 1
    by
        N1
end rule

rule resolveBracket
    replace [expression]
        (N1 [number])
    by
        N1
end rule

rule resolveDouble
    replace [expression]
        N1 [number] + N1
    by
        (2*N1)
end rule

rule resolveDoubleDivision
    replace [expression]
        N1 [number] / N1
    by
        1
end rule