app'(app'(eq, 0), 0) → true
app'(app'(eq, 0), app'(s, x)) → false
app'(app'(eq, app'(s, x)), 0) → false
app'(app'(eq, app'(s, x)), app'(s, y)) → app'(app'(eq, x), y)
app'(app'(le, 0), y) → true
app'(app'(le, app'(s, x)), 0) → false
app'(app'(le, app'(s, x)), app'(s, y)) → app'(app'(le, x), y)
app'(app'(app, nil), y) → y
app'(app'(app, app'(app'(add, n), x)), y) → app'(app'(add, n), app'(app'(app, x), y))
app'(min, app'(app'(add, n), nil)) → n
app'(min, app'(app'(add, n), app'(app'(add, m), x))) → app'(app'(if_min, app'(app'(le, n), m)), app'(app'(add, n), app'(app'(add, m), x)))
app'(app'(if_min, true), app'(app'(add, n), app'(app'(add, m), x))) → app'(min, app'(app'(add, n), x))
app'(app'(if_min, false), app'(app'(add, n), app'(app'(add, m), x))) → app'(min, app'(app'(add, m), x))
app'(app'(rm, n), nil) → nil
app'(app'(rm, n), app'(app'(add, m), x)) → app'(app'(app'(if_rm, app'(app'(eq, n), m)), n), app'(app'(add, m), x))
app'(app'(app'(if_rm, true), n), app'(app'(add, m), x)) → app'(app'(rm, n), x)
app'(app'(app'(if_rm, false), n), app'(app'(add, m), x)) → app'(app'(add, m), app'(app'(rm, n), x))
app'(app'(minsort, nil), nil) → nil
app'(app'(minsort, app'(app'(add, n), x)), y) → app'(app'(app'(if_minsort, app'(app'(eq, n), app'(min, app'(app'(add, n), x)))), app'(app'(add, n), x)), y)
app'(app'(app'(if_minsort, true), app'(app'(add, n), x)), y) → app'(app'(add, n), app'(app'(minsort, app'(app'(app, app'(app'(rm, n), x)), y)), nil))
app'(app'(app'(if_minsort, false), app'(app'(add, n), x)), y) → app'(app'(minsort, x), app'(app'(add, n), y))
app'(app'(map, f), nil) → nil
app'(app'(map, f), app'(app'(add, x), xs)) → app'(app'(add, app'(f, x)), app'(app'(map, f), xs))
app'(app'(filter, f), nil) → nil
app'(app'(filter, f), app'(app'(add, x), xs)) → app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs)
app'(app'(app'(app'(filter2, true), f), x), xs) → app'(app'(add, x), app'(app'(filter, f), xs))
app'(app'(app'(app'(filter2, false), f), x), xs) → app'(app'(filter, f), xs)

↳ QTRS

app'(app'(eq, 0), 0) → true
app'(app'(eq, 0), app'(s, x)) → false
app'(app'(eq, app'(s, x)), 0) → false
app'(app'(eq, app'(s, x)), app'(s, y)) → app'(app'(eq, x), y)
app'(app'(le, 0), y) → true
app'(app'(le, app'(s, x)), 0) → false
app'(app'(le, app'(s, x)), app'(s, y)) → app'(app'(le, x), y)
app'(app'(app, nil), y) → y
app'(app'(app, app'(app'(add, n), x)), y) → app'(app'(add, n), app'(app'(app, x), y))
app'(min, app'(app'(add, n), nil)) → n
app'(min, app'(app'(add, n), app'(app'(add, m), x))) → app'(app'(if_min, app'(app'(le, n), m)), app'(app'(add, n), app'(app'(add, m), x)))
app'(app'(if_min, true), app'(app'(add, n), app'(app'(add, m), x))) → app'(min, app'(app'(add, n), x))
app'(app'(if_min, false), app'(app'(add, n), app'(app'(add, m), x))) → app'(min, app'(app'(add, m), x))
app'(app'(rm, n), nil) → nil
app'(app'(rm, n), app'(app'(add, m), x)) → app'(app'(app'(if_rm, app'(app'(eq, n), m)), n), app'(app'(add, m), x))
app'(app'(app'(if_rm, true), n), app'(app'(add, m), x)) → app'(app'(rm, n), x)
app'(app'(app'(if_rm, false), n), app'(app'(add, m), x)) → app'(app'(add, m), app'(app'(rm, n), x))
app'(app'(minsort, nil), nil) → nil
app'(app'(minsort, app'(app'(add, n), x)), y) → app'(app'(app'(if_minsort, app'(app'(eq, n), app'(min, app'(app'(add, n), x)))), app'(app'(add, n), x)), y)
app'(app'(app'(if_minsort, true), app'(app'(add, n), x)), y) → app'(app'(add, n), app'(app'(minsort, app'(app'(app, app'(app'(rm, n), x)), y)), nil))
app'(app'(app'(if_minsort, false), app'(app'(add, n), x)), y) → app'(app'(minsort, x), app'(app'(add, n), y))
app'(app'(map, f), nil) → nil
app'(app'(map, f), app'(app'(add, x), xs)) → app'(app'(add, app'(f, x)), app'(app'(map, f), xs))
app'(app'(filter, f), nil) → nil
app'(app'(filter, f), app'(app'(add, x), xs)) → app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs)
app'(app'(app'(app'(filter2, true), f), x), xs) → app'(app'(add, x), app'(app'(filter, f), xs))
app'(app'(app'(app'(filter2, false), f), x), xs) → app'(app'(filter, f), xs)