MAYBE

Problem:
 app(app(apply(),f_1),x) -> app(f_1,x)
 app(id(),x) -> x
 app(app(app(uncurry(),f_2),x),y) -> app(app(f_2,x),y)
 app(app(app(swap(),f_2),y),x) -> app(app(f_2,x),y)
 app(app(app(compose(),g_1),f_1),x) -> app(g_1,app(f_1,x))
 app(app(const(),x),y) -> x
 app(listify(),x) -> app(app(cons(),x),nil())
 app(app(app(app(fold(),f_3),g_2),x),nil()) -> x
 app(app(app(app(fold(),f_3),g_2),x),app(app(cons(),z),t)) ->
 app(app(f_3,app(g_2,z)),app(app(app(app(fold(),f_3),g_2),x),t))
 app(sum(),l) -> app(app(app(app(fold(),add()),id()),0()),l)
 app(app(uncurry(),app(app(fold(),cons()),id())),nil()) -> id()
 append() -> app(app(compose(),app(app(swap(),fold()),cons())),id())
 reverse() -> app(app(uncurry(),app(app(fold(),app(swap(),append())),listify())),nil())
 length() -> app(app(uncurry(),app(app(fold(),add()),app(cons(),1()))),0())

Proof:
 Open