R
↳Dependency Pair Analysis
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)
APP(app(app(comp, f), g), x) -> APP(f, app(g, x))
APP(app(app(comp, f), g), x) -> APP(g, x)
APP(twice, f) -> APP(app(comp, f), f)
APP(twice, f) -> APP(comp, f)
R
↳DPs
→DP Problem 1
↳Narrowing Transformation
APP(twice, f) -> APP(app(comp, f), f)
APP(app(app(comp, f), g), x) -> APP(g, x)
APP(app(app(comp, f), g), x) -> APP(f, app(g, x))
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(map, f), nil) -> nil
app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(app(comp, f), g), x) -> app(f, app(g, x))
app(twice, f) -> app(app(comp, f), f)
innermost
no new Dependency Pairs are created.
APP(twice, f) -> APP(app(comp, f), f)
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Narrowing Transformation
APP(app(app(comp, f), g), x) -> APP(f, app(g, x))
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(app(comp, f), g), x) -> APP(g, x)
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))
app(app(app(comp, f), g), x) -> app(f, app(g, x))
app(twice, f) -> app(app(comp, f), f)
innermost
six new Dependency Pairs are created:
APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs))
APP(app(map, app(map, f'')), app(app(cons, nil), xs)) -> APP(app(cons, nil), app(app(map, app(map, f'')), xs))
APP(app(map, app(map, f'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(cons, app(app(cons, app(f'', x'')), app(app(map, f''), xs''))), app(app(map, app(map, f'')), xs))
APP(app(map, app(app(comp, f''), g')), app(app(cons, x''), xs)) -> APP(app(cons, app(f'', app(g', x''))), app(app(map, app(app(comp, f''), g')), xs))
APP(app(map, twice), app(app(cons, x'), xs)) -> APP(app(cons, app(app(comp, x'), x')), app(app(map, twice), xs))
APP(app(map, f''), app(app(cons, x), nil)) -> APP(app(cons, app(f'', x)), nil)
APP(app(map, f''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(cons, app(f'', x)), app(app(cons, app(f'', x'')), app(app(map, f''), xs'')))
R
↳DPs
→DP Problem 1
↳Nar
→DP Problem 2
↳Nar
...
→DP Problem 3
↳Remaining Obligation(s)
APP(app(map, f''), app(app(cons, x), app(app(cons, x''), xs''))) -> APP(app(cons, app(f'', x)), app(app(cons, app(f'', x'')), app(app(map, f''), xs'')))
APP(app(map, f''), app(app(cons, x), nil)) -> APP(app(cons, app(f'', x)), nil)
APP(app(map, twice), app(app(cons, x'), xs)) -> APP(app(cons, app(app(comp, x'), x')), app(app(map, twice), xs))
APP(app(map, app(app(comp, f''), g')), app(app(cons, x''), xs)) -> APP(app(cons, app(f'', app(g', x''))), app(app(map, app(app(comp, f''), g')), xs))
APP(app(app(comp, f), g), x) -> APP(g, x)
APP(app(map, app(map, f'')), app(app(cons, app(app(cons, x''), xs'')), xs)) -> APP(app(cons, app(app(cons, app(f'', x'')), app(app(map, f''), xs''))), app(app(map, app(map, f'')), xs))
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(app(comp, f), g), x) -> APP(f, app(g, x))
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))
app(app(app(comp, f), g), x) -> app(f, app(g, x))
app(twice, f) -> app(app(comp, f), f)
innermost