(VAR fun u x xs y z )
(RULES 
        app(perfectp,0) -> false
        app(perfectp,app(s,x)) -> app(app(app(app(f,x),app(s,0)),app(s,x)),app(s,x))
        app(app(app(app(f,0),y),0),u) -> true
        app(app(app(app(f,0),y),app(s,z)),u) -> false
        app(app(app(app(f,app(s,x)),0),z),u) -> app(app(app(app(f,x),u),app(app(minus,z),app(s,x))),u)
        app(app(app(app(f,app(s,x)),app(s,y)),z),u) -> app(app(app(if,app(app(le,x),y)),app(app(app(app(f,app(s,x)),app(app(minus,y),x)),z),u)),app(app(app(app(f,x),u),z),u))
        app(app(map,fun),nil) -> nil
        app(app(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs))
        app(app(filter,fun),nil) -> nil
        app(app(filter,fun),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(fun,x)),fun),x),xs)
        app(app(app(app(filter2,true),fun),x),xs) -> app(app(cons,x),app(app(filter,fun),xs))
        app(app(app(app(filter2,false),fun),x),xs) -> app(app(filter,fun),xs)
        
)