(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< 0, true, s(X), false, nil, cons(X, X) >)
(SIGNATURES
    le :: [A x A] -> A
    eq :: [A x A] -> A
    if :: [A x A x A] -> A
    minsort :: [A] -> A
    min :: [A x A] -> A
    del :: [A x A] -> A)
(RULES
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    eq(0(),0()) -> true()
    eq(0(),s(y)) -> false()
    eq(s(x),0()) -> false()
    eq(s(x),s(y)) -> eq(x,y)
    if(true(),x,y) -> x
    if(false(),x,y) -> y
    minsort(nil()) -> nil()
    minsort(cons(x,y)) -> cons(min(x
                                  ,y)
                              ,minsort(del(min(x,y)
                                          ,cons(x,y))))
    min(x,nil()) -> x
    min(x,cons(y,z)) -> if(le(x,y)
                          ,min(x,z)
                          ,min(y,z))
    del(x,nil()) -> nil()
    del(x,cons(y,z)) -> if(eq(x,y)
                          ,z
                          ,cons(y,del(x,z))))