Problem AProVE 08 parting04 maxsort h

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 08 parting04 maxsort h

stdout:

MAYBE

Problem:
max(nil()) -> 0()
max(cons(x,nil())) -> x
max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
if1(true(),x,y,xs) -> max(cons(x,xs))
if1(false(),x,y,xs) -> max(cons(y,xs))
del(x,nil()) -> nil()
del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
if2(true(),x,y,xs) -> xs
if2(false(),x,y,xs) -> cons(y,del(x,xs))
eq(0(),0()) -> true()
eq(0(),s(y)) -> false()
eq(s(x),0()) -> false()
eq(s(x),s(y)) -> eq(x,y)
sort(nil()) -> nil()
sort(cons(x,xs)) -> cons(max(cons(x,xs)),sort(h(del(max(cons(x,xs)),cons(x,xs)))))
ge(0(),0()) -> true()
ge(s(x),0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),s(y)) -> ge(x,y)
h(nil()) -> nil()
h(cons(x,xs)) -> cons(x,h(xs))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 08 parting04 maxsort h

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 08 parting04 maxsort h

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  max(nil()) -> 0()
     , max(cons(x, nil())) -> x
     , max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs)
     , if1(true(), x, y, xs) -> max(cons(x, xs))
     , if1(false(), x, y, xs) -> max(cons(y, xs))
     , del(x, nil()) -> nil()
     , del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
     , if2(true(), x, y, xs) -> xs
     , if2(false(), x, y, xs) -> cons(y, del(x, xs))
     , eq(0(), 0()) -> true()
     , eq(0(), s(y)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(s(x), s(y)) -> eq(x, y)
     , sort(nil()) -> nil()
     , sort(cons(x, xs)) ->
       cons(max(cons(x, xs)), sort(h(del(max(cons(x, xs)), cons(x, xs)))))
     , ge(0(), 0()) -> true()
     , ge(s(x), 0()) -> true()
     , ge(0(), s(x)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , h(nil()) -> nil()
     , h(cons(x, xs)) -> cons(x, h(xs))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 08 parting04 maxsort h

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 08 parting04 maxsort h

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  max(nil()) -> 0()
     , max(cons(x, nil())) -> x
     , max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs)
     , if1(true(), x, y, xs) -> max(cons(x, xs))
     , if1(false(), x, y, xs) -> max(cons(y, xs))
     , del(x, nil()) -> nil()
     , del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs)
     , if2(true(), x, y, xs) -> xs
     , if2(false(), x, y, xs) -> cons(y, del(x, xs))
     , eq(0(), 0()) -> true()
     , eq(0(), s(y)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(s(x), s(y)) -> eq(x, y)
     , sort(nil()) -> nil()
     , sort(cons(x, xs)) ->
       cons(max(cons(x, xs)), sort(h(del(max(cons(x, xs)), cons(x, xs)))))
     , ge(0(), 0()) -> true()
     , ge(s(x), 0()) -> true()
     , ge(0(), s(x)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , h(nil()) -> nil()
     , h(cons(x, xs)) -> cons(x, h(xs))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds