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(x,nil())) -> x
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))
empty(nil()) -> true()
empty(cons(n,x)) -> false()
head(cons(n,x)) -> n
tail(nil()) -> nil()
tail(cons(n,x)) -> x
sort(x) -> sortIter(x,nil())
sortIter(x,y) -> if(empty(x),x,y,append(y,cons(min(x),nil())))
if(true(),x,y,z) -> y
if(false(),x,y,z) -> sortIter(replace(min(x),head(x),tail(x)),z)
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(x, nil())) -> x
, 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))
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, head(cons(n, x)) -> n
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, sort(x) -> sortIter(x, nil())
, sortIter(x, y) ->
if(empty(x), x, y, append(y, cons(min(x), nil())))
, if(true(), x, y, z) -> y
, if(false(), x, y, z) ->
sortIter(replace(min(x), head(x), tail(x)), z)}
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(x, nil())) -> x
, 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))
, empty(nil()) -> true()
, empty(cons(n, x)) -> false()
, head(cons(n, x)) -> n
, tail(nil()) -> nil()
, tail(cons(n, x)) -> x
, sort(x) -> sortIter(x, nil())
, sortIter(x, y) ->
if(empty(x), x, y, append(y, cons(min(x), nil())))
, if(true(), x, y, z) -> y
, if(false(), x, y, z) ->
sortIter(replace(min(x), head(x), tail(x)), z)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds