Tool CaT
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:
OpenTool IRC1
stdout:
MAYBE
Tool IRC2
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 secondsTool RC1
stdout:
MAYBE
Tool RC2
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