R
↳Dependency Pair Analysis
APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)
APP(app(f, 0), n) -> APP(hd, app(app(map, f), app(app(cons, 0), nil)))
APP(app(f, 0), n) -> APP(app(map, f), app(app(cons, 0), nil))
APP(app(f, 0), n) -> APP(map, f)
APP(app(f, 0), n) -> APP(app(cons, 0), nil)
APP(app(f, 0), n) -> APP(cons, 0)
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs))
APP(app(map, f), app(app(cons, x), xs)) -> APP(cons, app(f, x))
APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs)
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs)
APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs))
APP(app(f, 0), n) -> APP(app(cons, 0), nil)
APP(app(f, 0), n) -> APP(app(map, f), app(app(cons, 0), nil))
APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)
app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)
app(app(map, f), nil) -> nil
app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
three new Dependency Pairs are created:
APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)
APP(app(0, 0), n) -> APP(app(hd, app(app(hd, app(app(map, map), app(app(cons, 0), nil))), app(app(cons, 0), nil))), n)
APP(app(f'', 0), n) -> APP(app(hd, app(app(cons, app(f'', 0)), app(app(map, f''), nil))), n)
APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(hd, app(app(map, cons), app(app(cons, 0), nil))), nil))), n)
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Remaining Obligation(s)
APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(hd, app(app(map, cons), app(app(cons, 0), nil))), nil))), n)
APP(app(f'', 0), n) -> APP(app(hd, app(app(cons, app(f'', 0)), app(app(map, f''), nil))), n)
APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs))
APP(app(0, 0), n) -> APP(app(hd, app(app(hd, app(app(map, map), app(app(cons, 0), nil))), app(app(cons, 0), nil))), n)
APP(app(f, 0), n) -> APP(app(cons, 0), nil)
APP(app(f, 0), n) -> APP(app(map, f), app(app(cons, 0), nil))
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs)
app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)
app(app(map, f), nil) -> nil
app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))