Problem AG01 innermost 4.36

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AG01 innermost 4.36

stdout:

MAYBE

Problem:
eq(0(),0()) -> true()
eq(0(),s(m)) -> false()
eq(s(n),0()) -> false()
eq(s(n),s(m)) -> eq(n,m)
le(0(),m) -> true()
le(s(n),0()) -> false()
le(s(n),s(m)) -> le(n,m)
min(cons(0(),nil())) -> 0()
min(cons(s(n),nil())) -> s(n)
min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x)))
if_min(true(),cons(n,cons(m,x))) -> min(cons(n,x))
if_min(false(),cons(n,cons(m,x))) -> min(cons(m,x))
replace(n,m,nil()) -> nil()
replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x))
if_replace(true(),n,m,cons(k,x)) -> cons(m,x)
if_replace(false(),n,m,cons(k,x)) -> cons(k,replace(n,m,x))
sort(nil()) -> nil()
sort(cons(n,x)) -> cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x)))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AG01 innermost 4.36

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 innermost 4.36

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  eq(0(), 0()) -> true()
     , eq(0(), s(m)) -> false()
     , eq(s(n), 0()) -> false()
     , eq(s(n), s(m)) -> eq(n, m)
     , le(0(), m) -> true()
     , le(s(n), 0()) -> false()
     , le(s(n), s(m)) -> le(n, m)
     , min(cons(0(), nil())) -> 0()
     , min(cons(s(n), nil())) -> s(n)
     , min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x)))
     , if_min(true(), cons(n, cons(m, x))) -> min(cons(n, x))
     , if_min(false(), cons(n, cons(m, x))) -> min(cons(m, x))
     , replace(n, m, nil()) -> nil()
     , replace(n, m, cons(k, x)) ->
       if_replace(eq(n, k), n, m, cons(k, x))
     , if_replace(true(), n, m, cons(k, x)) -> cons(m, x)
     , if_replace(false(), n, m, cons(k, x)) ->
       cons(k, replace(n, m, x))
     , sort(nil()) -> nil()
     , sort(cons(n, x)) ->
       cons(min(cons(n, x)), sort(replace(min(cons(n, x)), n, x)))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AG01 innermost 4.36

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 innermost 4.36

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  eq(0(), 0()) -> true()
     , eq(0(), s(m)) -> false()
     , eq(s(n), 0()) -> false()
     , eq(s(n), s(m)) -> eq(n, m)
     , le(0(), m) -> true()
     , le(s(n), 0()) -> false()
     , le(s(n), s(m)) -> le(n, m)
     , min(cons(0(), nil())) -> 0()
     , min(cons(s(n), nil())) -> s(n)
     , min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x)))
     , if_min(true(), cons(n, cons(m, x))) -> min(cons(n, x))
     , if_min(false(), cons(n, cons(m, x))) -> min(cons(m, x))
     , replace(n, m, nil()) -> nil()
     , replace(n, m, cons(k, x)) ->
       if_replace(eq(n, k), n, m, cons(k, x))
     , if_replace(true(), n, m, cons(k, x)) -> cons(m, x)
     , if_replace(false(), n, m, cons(k, x)) ->
       cons(k, replace(n, m, x))
     , sort(nil()) -> nil()
     , sort(cons(n, x)) ->
       cons(min(cons(n, x)), sort(replace(min(cons(n, x)), n, x)))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds