(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< nil, .(X, X), if(X, X, X), =(X, X) >)
(SIGNATURES
    purge :: [A] -> A
    remove :: [A x A] -> A)
(RULES
    purge(nil()) -> nil()
    purge(.(x,y)) -> .(x
                      ,purge(remove(x,y)))
    remove(x,nil()) -> nil()
    remove(x,.(y,z)) -> if(=(x,y)
                          ,remove(x,z)
                          ,.(y,remove(x,z))))