(VAR X X1 X2 X3 Y )
(RULES 
        a__minus(0, Y) -> 0
        a__minus(s(X), s(Y)) -> a__minus(X, Y)
        a__geq(X, 0) -> true
        a__geq(0, s(Y)) -> false
        a__geq(s(X), s(Y)) -> a__geq(X, Y)
        a__div(0, s(Y)) -> 0
        a__div(s(X), s(Y)) -> a__if(a__geq(X, Y), s(div(minus(X, Y), s(Y))), 0)
        a__if(true, X, Y) -> mark(X)
        a__if(false, X, Y) -> mark(Y)
        mark(minus(X1, X2)) -> a__minus(X1, X2)
        mark(geq(X1, X2)) -> a__geq(X1, X2)
        mark(div(X1, X2)) -> a__div(mark(X1), X2)
        mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
        mark(0) -> 0
        mark(s(X)) -> s(mark(X))
        mark(true) -> true
        mark(false) -> false
        a__minus(X1, X2) -> minus(X1, X2)
        a__geq(X1, X2) -> geq(X1, X2)
        a__div(X1, X2) -> div(X1, X2)
        a__if(X1, X2, X3) -> if(X1, X2, X3)
        
)