Problem AProVE 09 Inductive maxsortcondition

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive maxsortcondition

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(xs) -> if3(empty(xs),xs)
if3(true(),xs) -> nil()
if3(false(),xs) -> sort(del(max(xs),xs))
empty(nil()) -> true()
empty(cons(x,xs)) -> false()
ge(x,0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),s(y)) -> ge(x,y)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive maxsortcondition

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive maxsortcondition

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(xs) -> if3(empty(xs), xs)
     , if3(true(), xs) -> nil()
     , if3(false(), xs) -> sort(del(max(xs), xs))
     , empty(nil()) -> true()
     , empty(cons(x, xs)) -> false()
     , ge(x, 0()) -> true()
     , ge(0(), s(x)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive maxsortcondition

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive maxsortcondition

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(xs) -> if3(empty(xs), xs)
     , if3(true(), xs) -> nil()
     , if3(false(), xs) -> sort(del(max(xs), xs))
     , empty(nil()) -> true()
     , empty(cons(x, xs)) -> false()
     , ge(x, 0()) -> true()
     , ge(0(), s(x)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds