Problem AProVE 09 Inductive qsortlast

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive qsortlast

stdout:

MAYBE

Problem:
qsort(nil()) -> nil()
qsort(cons(x,xs)) ->
append(qsort(filterlow(last(cons(x,xs)),cons(x,xs))),cons(last(cons(x,xs)),
qsort(filterhigh
(last(cons(x,xs)),cons(x,xs)))))
filterlow(n,nil()) -> nil()
filterlow(n,cons(x,xs)) -> if1(ge(n,x),n,x,xs)
if1(true(),n,x,xs) -> filterlow(n,xs)
if1(false(),n,x,xs) -> cons(x,filterlow(n,xs))
filterhigh(n,nil()) -> nil()
filterhigh(n,cons(x,xs)) -> if2(ge(x,n),n,x,xs)
if2(true(),n,x,xs) -> filterhigh(n,xs)
if2(false(),n,x,xs) -> cons(x,filterhigh(n,xs))
ge(x,0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),s(y)) -> ge(x,y)
append(nil(),ys()) -> ys()
append(cons(x,xs),ys()) -> cons(x,append(xs,ys()))
last(nil()) -> 0()
last(cons(x,nil())) -> x
last(cons(x,cons(y,xs))) -> last(cons(y,xs))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive qsortlast

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive qsortlast

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  qsort(nil()) -> nil()
     , qsort(cons(x, xs)) ->
       append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
              cons(last(cons(x, xs)),
                   qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
     , filterlow(n, nil()) -> nil()
     , filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
     , if1(true(), n, x, xs) -> filterlow(n, xs)
     , if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
     , filterhigh(n, nil()) -> nil()
     , filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
     , if2(true(), n, x, xs) -> filterhigh(n, xs)
     , if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs))
     , ge(x, 0()) -> true()
     , ge(0(), s(x)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , append(nil(), ys()) -> ys()
     , append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
     , last(nil()) -> 0()
     , last(cons(x, nil())) -> x
     , last(cons(x, cons(y, xs))) -> last(cons(y, xs))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive qsortlast

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive qsortlast

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  qsort(nil()) -> nil()
     , qsort(cons(x, xs)) ->
       append(qsort(filterlow(last(cons(x, xs)), cons(x, xs))),
              cons(last(cons(x, xs)),
                   qsort(filterhigh(last(cons(x, xs)), cons(x, xs)))))
     , filterlow(n, nil()) -> nil()
     , filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs)
     , if1(true(), n, x, xs) -> filterlow(n, xs)
     , if1(false(), n, x, xs) -> cons(x, filterlow(n, xs))
     , filterhigh(n, nil()) -> nil()
     , filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
     , if2(true(), n, x, xs) -> filterhigh(n, xs)
     , if2(false(), n, x, xs) -> cons(x, filterhigh(n, xs))
     , ge(x, 0()) -> true()
     , ge(0(), s(x)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , append(nil(), ys()) -> ys()
     , append(cons(x, xs), ys()) -> cons(x, append(xs, ys()))
     , last(nil()) -> 0()
     , last(cons(x, nil())) -> x
     , last(cons(x, cons(y, xs))) -> last(cons(y, xs))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds