Problem AProVE 09 Inductive minsort

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive minsort

stdout:

MAYBE

Problem:
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
eq(0(),0()) -> true()
eq(0(),s(y)) -> false()
eq(s(x),0()) -> false()
eq(s(x),s(y)) -> eq(x,y)
minsort(nil()) -> nil()
minsort(cons(x,xs)) -> cons(min(cons(x,xs)),minsort(rm(min(cons(x,xs)),cons(x,xs))))
min(nil()) -> 0()
min(cons(x,nil())) -> x
min(cons(x,cons(y,xs))) -> if1(le(x,y),x,y,xs)
if1(true(),x,y,xs) -> min(cons(x,xs))
if1(false(),x,y,xs) -> min(cons(y,xs))
rm(x,nil()) -> nil()
rm(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
if2(true(),x,y,xs) -> rm(x,xs)
if2(false(),x,y,xs) -> cons(y,rm(x,xs))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive minsort

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive minsort

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 09 Inductive minsort

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 09 Inductive minsort

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds