R
↳Dependency Pair Analysis
APP(app(sub, app(s, x)), app(s, y)) -> APP(app(sub, x), y)
APP(app(sub, app(s, x)), app(s, y)) -> APP(sub, x)
APP(app(gtr, app(s, x)), app(s, y)) -> APP(app(gtr, x), y)
APP(app(gtr, app(s, x)), app(s, y)) -> APP(gtr, x)
APP(app(d, app(s, x)), app(s, y)) -> APP(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x)))
APP(app(d, app(s, x)), app(s, y)) -> APP(app(if, app(app(gtr, x), y)), false)
APP(app(d, app(s, x)), app(s, y)) -> APP(if, app(app(gtr, x), y))
APP(app(d, app(s, x)), app(s, y)) -> APP(app(gtr, x), y)
APP(app(d, app(s, x)), app(s, y)) -> APP(gtr, x)
APP(app(d, app(s, x)), app(s, y)) -> APP(app(d, app(s, x)), app(app(sub, y), x))
APP(app(d, app(s, x)), app(s, y)) -> APP(app(sub, y), x)
APP(app(d, app(s, x)), app(s, y)) -> APP(sub, y)
APP(len, app(app(cons, x), xs)) -> APP(s, app(len, xs))
APP(len, app(app(cons, x), xs)) -> APP(len, xs)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs)))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(if, app(p, x))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(cons, x), app(app(filter, p), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳Remaining
APP(len, app(app(cons, x), xs)) -> APP(len, xs)
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(sub, x), 0) -> x
app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y)
app(app(gtr, 0), y) -> false
app(app(gtr, app(s, x)), 0) -> true
app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y)
app(app(d, x), 0) -> true
app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x)))
app(len, nil) -> 0
app(len, app(app(cons, x), xs)) -> app(s, app(len, xs))
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
APP(len, app(app(cons, x), xs)) -> APP(len, xs)
APP(x1, x2) -> APP(x1, x2)
app(x1, x2) -> app(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 3
↳Dependency Graph
→DP Problem 2
↳Remaining
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(sub, x), 0) -> x
app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y)
app(app(gtr, 0), y) -> false
app(app(gtr, app(s, x)), 0) -> true
app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y)
app(app(d, x), 0) -> true
app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x)))
app(len, nil) -> 0
app(len, app(app(cons, x), xs)) -> app(s, app(len, xs))
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Remaining Obligation(s)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(filter, p), xs)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(cons, x), app(app(filter, p), xs))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(p, x)
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs)))
APP(app(filter, p), app(app(cons, x), xs)) -> APP(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))
APP(app(d, app(s, x)), app(s, y)) -> APP(app(sub, y), x)
APP(app(d, app(s, x)), app(s, y)) -> APP(app(d, app(s, x)), app(app(sub, y), x))
APP(app(d, app(s, x)), app(s, y)) -> APP(app(gtr, x), y)
APP(app(d, app(s, x)), app(s, y)) -> APP(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x)))
APP(app(gtr, app(s, x)), app(s, y)) -> APP(app(gtr, x), y)
APP(app(sub, app(s, x)), app(s, y)) -> APP(app(sub, x), y)
app(app(app(if, true), xs), ys) -> xs
app(app(app(if, false), xs), ys) -> ys
app(app(sub, x), 0) -> x
app(app(sub, app(s, x)), app(s, y)) -> app(app(sub, x), y)
app(app(gtr, 0), y) -> false
app(app(gtr, app(s, x)), 0) -> true
app(app(gtr, app(s, x)), app(s, y)) -> app(app(gtr, x), y)
app(app(d, x), 0) -> true
app(app(d, app(s, x)), app(s, y)) -> app(app(app(if, app(app(gtr, x), y)), false), app(app(d, app(s, x)), app(app(sub, y), x)))
app(len, nil) -> 0
app(len, app(app(cons, x), xs)) -> app(s, app(len, xs))
app(app(filter, p), nil) -> nil
app(app(filter, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(filter, p), xs))), app(app(filter, p), xs))