Tool CaT
stdout:
MAYBE
Problem:
isEmpty(empty()) -> true()
isEmpty(node(l,r)) -> false()
left(empty()) -> empty()
left(node(l,r)) -> l
right(empty()) -> empty()
right(node(l,r)) -> r
inc(0()) -> s(0())
inc(s(x)) -> s(inc(x))
count(n,x) ->
if(isEmpty(n),isEmpty(left(n)),right(n),node(left(left(n)),node(right(left(n)),right(n))),x,inc(x))
if(true(),b,n,m,x,y) -> x
if(false(),false(),n,m,x,y) -> count(m,x)
if(false(),true(),n,m,x,y) -> count(n,y)
nrOfNodes(n) -> count(n,0())
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:
{ isEmpty(empty()) -> true()
, isEmpty(node(l, r)) -> false()
, left(empty()) -> empty()
, left(node(l, r)) -> l
, right(empty()) -> empty()
, right(node(l, r)) -> r
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, count(n, x) ->
if(isEmpty(n),
isEmpty(left(n)),
right(n),
node(left(left(n)), node(right(left(n)), right(n))),
x,
inc(x))
, if(true(), b, n, m, x, y) -> x
, if(false(), false(), n, m, x, y) -> count(m, x)
, if(false(), true(), n, m, x, y) -> count(n, y)
, nrOfNodes(n) -> count(n, 0())}
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:
{ isEmpty(empty()) -> true()
, isEmpty(node(l, r)) -> false()
, left(empty()) -> empty()
, left(node(l, r)) -> l
, right(empty()) -> empty()
, right(node(l, r)) -> r
, inc(0()) -> s(0())
, inc(s(x)) -> s(inc(x))
, count(n, x) ->
if(isEmpty(n),
isEmpty(left(n)),
right(n),
node(left(left(n)), node(right(left(n)), right(n))),
x,
inc(x))
, if(true(), b, n, m, x, y) -> x
, if(false(), false(), n, m, x, y) -> count(m, x)
, if(false(), true(), n, m, x, y) -> count(n, y)
, nrOfNodes(n) -> count(n, 0())}
Proof Output:
Computation stopped due to timeout after 60.0 seconds