(STRATEGY
    INNERMOST)

(VAR
    x xs y ys z)
(DATATYPES
    A = µX.< s(X), 0, false, true, logError, nil, cons(X, X), error, b, c >)
(SIGNATURES
    le :: [A x A] -> A
    double :: [A] -> A
    log :: [A] -> A
    loop :: [A x A x A] -> A
    if :: [A x A x A x A] -> A
    maplog :: [A] -> A
    mapIter :: [A x A] -> A
    ifmap :: [A x A x A] -> A
    isempty :: [A] -> A
    last :: [A] -> A
    droplast :: [A] -> A
    a :: [] -> A)
(RULES
    le(s(x),0()) -> false()
    le(0(),y) -> true()
    le(s(x),s(y)) -> le(x,y)
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
    log(0()) -> logError()
    log(s(x)) -> loop(s(x)
                     ,s(0())
                     ,0())
    loop(x,s(y),z) -> if(le(x,s(y))
                        ,x
                        ,s(y)
                        ,z)
    if(true(),x,y,z) -> z
    if(false(),x,y,z) -> loop(x
                             ,double(y)
                             ,s(z))
    maplog(xs) -> mapIter(xs,nil())
    mapIter(xs,ys) ->
      ifmap(isempty(xs),xs,ys)
    ifmap(true(),xs,ys) -> ys
    ifmap(false(),xs,ys) ->
      mapIter(droplast(xs)
             ,cons(log(last(xs)),ys))
    isempty(nil()) -> true()
    isempty(cons(x,xs)) -> false()
    last(nil()) -> error()
    last(cons(x,nil())) -> x
    last(cons(x,cons(y,xs))) ->
      last(cons(y,xs))
    droplast(nil()) -> nil()
    droplast(cons(x,nil())) -> nil()
    droplast(cons(x,cons(y,xs))) ->
      cons(x,droplast(cons(y,xs)))
    a() -> b()
    a() -> c())