R
↳Dependency Pair Analysis
APP(app(app(compose, f), g), x) -> APP(g, app(f, x))
APP(app(app(compose, f), g), x) -> APP(f, x)
APP(reverse, l) -> APP(app(reverse2, l), nil)
APP(reverse, l) -> APP(reverse2, l)
APP(app(reverse2, app(app(cons, x), xs)), l) -> APP(app(reverse2, xs), app(app(cons, x), l))
APP(app(reverse2, app(app(cons, x), xs)), l) -> APP(reverse2, xs)
APP(app(reverse2, app(app(cons, x), xs)), l) -> APP(app(cons, x), l)
LAST -> APP(app(compose, hd), reverse)
LAST -> APP(compose, hd)
INIT -> APP(app(compose, reverse), app(app(compose, tl), reverse))
INIT -> APP(compose, reverse)
INIT -> APP(app(compose, tl), reverse)
INIT -> APP(compose, tl)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
APP(app(reverse2, app(app(cons, x), xs)), l) -> APP(app(reverse2, xs), app(app(cons, x), l))
APP(reverse, l) -> APP(app(reverse2, l), nil)
APP(app(app(compose, f), g), x) -> APP(f, x)
APP(app(app(compose, f), g), x) -> APP(g, app(f, x))
app(app(app(compose, f), g), x) -> app(g, app(f, x))
app(reverse, l) -> app(app(reverse2, l), nil)
app(app(reverse2, nil), l) -> l
app(app(reverse2, app(app(cons, x), xs)), l) -> app(app(reverse2, xs), app(app(cons, x), l))
app(hd, app(app(cons, x), xs)) -> x
app(tl, app(app(cons, x), xs)) -> xs
last -> app(app(compose, hd), reverse)
init -> app(app(compose, reverse), app(app(compose, tl), reverse))
innermost
APP(app(app(compose, f), g), x) -> APP(f, x)
APP(app(app(compose, f), g), x) -> APP(g, app(f, x))
app(app(app(compose, f), g), x) -> app(g, app(f, x))
app(reverse, l) -> app(app(reverse2, l), nil)
app(app(reverse2, nil), l) -> l
app(app(reverse2, app(app(cons, x), xs)), l) -> app(app(reverse2, xs), app(app(cons, x), l))
app(hd, app(app(cons, x), xs)) -> x
app(tl, app(app(cons, x), xs)) -> xs
POL(reverse) = 0 POL(cons) = 0 POL(hd) = 0 POL(nil) = 0 POL(tl) = 1 POL(compose) = 1 POL(APP(x1, x2)) = 1 + x1 + x2 POL(app(x1, x2)) = x1 + x2 POL(reverse2) = 0
APP(x1, x2) -> APP(x1, x2)
app(x1, x2) -> app(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Argument Filtering and Ordering
APP(app(reverse2, app(app(cons, x), xs)), l) -> APP(app(reverse2, xs), app(app(cons, x), l))
APP(reverse, l) -> APP(app(reverse2, l), nil)
app(app(app(compose, f), g), x) -> app(g, app(f, x))
app(reverse, l) -> app(app(reverse2, l), nil)
app(app(reverse2, nil), l) -> l
app(app(reverse2, app(app(cons, x), xs)), l) -> app(app(reverse2, xs), app(app(cons, x), l))
app(hd, app(app(cons, x), xs)) -> x
app(tl, app(app(cons, x), xs)) -> xs
last -> app(app(compose, hd), reverse)
init -> app(app(compose, reverse), app(app(compose, tl), reverse))
innermost
APP(reverse, l) -> APP(app(reverse2, l), nil)
app(app(app(compose, f), g), x) -> app(g, app(f, x))
app(reverse, l) -> app(app(reverse2, l), nil)
app(app(reverse2, nil), l) -> l
app(app(reverse2, app(app(cons, x), xs)), l) -> app(app(reverse2, xs), app(app(cons, x), l))
app(hd, app(app(cons, x), xs)) -> x
app(tl, app(app(cons, x), xs)) -> xs
POL(reverse) = 1 POL(cons) = 0 POL(hd) = 1 POL(nil) = 0 POL(tl) = 0 POL(compose) = 0 POL(APP(x1, x2)) = 1 + x1 + x2 POL(app(x1, x2)) = x1 + x2 POL(reverse2) = 0
APP(x1, x2) -> APP(x1, x2)
app(x1, x2) -> app(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
...
→DP Problem 3
↳Argument Filtering and Ordering
APP(app(reverse2, app(app(cons, x), xs)), l) -> APP(app(reverse2, xs), app(app(cons, x), l))
app(app(app(compose, f), g), x) -> app(g, app(f, x))
app(reverse, l) -> app(app(reverse2, l), nil)
app(app(reverse2, nil), l) -> l
app(app(reverse2, app(app(cons, x), xs)), l) -> app(app(reverse2, xs), app(app(cons, x), l))
app(hd, app(app(cons, x), xs)) -> x
app(tl, app(app(cons, x), xs)) -> xs
last -> app(app(compose, hd), reverse)
init -> app(app(compose, reverse), app(app(compose, tl), reverse))
innermost
APP(app(reverse2, app(app(cons, x), xs)), l) -> APP(app(reverse2, xs), app(app(cons, x), l))
app(app(app(compose, f), g), x) -> app(g, app(f, x))
app(reverse, l) -> app(app(reverse2, l), nil)
app(app(reverse2, nil), l) -> l
app(app(reverse2, app(app(cons, x), xs)), l) -> app(app(reverse2, xs), app(app(cons, x), l))
app(hd, app(app(cons, x), xs)) -> x
app(tl, app(app(cons, x), xs)) -> xs
POL(reverse) = 0 POL(cons) = 1 POL(hd) = 1 POL(nil) = 0 POL(tl) = 0 POL(compose) = 0 POL(app(x1, x2)) = x1 + x2 POL(reverse2) = 0
APP(x1, x2) -> x1
app(x1, x2) -> app(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳AFS
...
→DP Problem 4
↳Dependency Graph
app(app(app(compose, f), g), x) -> app(g, app(f, x))
app(reverse, l) -> app(app(reverse2, l), nil)
app(app(reverse2, nil), l) -> l
app(app(reverse2, app(app(cons, x), xs)), l) -> app(app(reverse2, xs), app(app(cons, x), l))
app(hd, app(app(cons, x), xs)) -> x
app(tl, app(app(cons, x), xs)) -> xs
last -> app(app(compose, hd), reverse)
init -> app(app(compose, reverse), app(app(compose, tl), reverse))
innermost