Tool CaT
stdout:
MAYBE
Problem:
min(0(),y) -> 0()
min(s(x),0()) -> 0()
min(s(x),s(y)) -> min(x,y)
len(nil()) -> 0()
len(cons(x,xs)) -> s(len(xs))
sum(x,0()) -> x
sum(x,s(y)) -> s(sum(x,y))
le(0(),x) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
take(0(),cons(y,ys)) -> y
take(s(x),cons(y,ys)) -> take(x,ys)
addList(x,y) -> if(le(0(),min(len(x),len(y))),0(),x,y,nil())
if(false(),c,x,y,z) -> z
if(true(),c,xs,ys,z) ->
if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),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:
{ min(0(), y) -> 0()
, min(s(x), 0()) -> 0()
, min(s(x), s(y)) -> min(x, y)
, len(nil()) -> 0()
, len(cons(x, xs)) -> s(len(xs))
, sum(x, 0()) -> x
, sum(x, s(y)) -> s(sum(x, y))
, le(0(), x) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, take(0(), cons(y, ys)) -> y
, take(s(x), cons(y, ys)) -> take(x, ys)
, addList(x, y) ->
if(le(0(), min(len(x), len(y))), 0(), x, y, nil())
, if(false(), c, x, y, z) -> z
, if(true(), c, xs, ys, z) ->
if(le(s(c), min(len(xs), len(ys))),
s(c),
xs,
ys,
cons(sum(take(c, xs), take(c, ys)), 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:
{ min(0(), y) -> 0()
, min(s(x), 0()) -> 0()
, min(s(x), s(y)) -> min(x, y)
, len(nil()) -> 0()
, len(cons(x, xs)) -> s(len(xs))
, sum(x, 0()) -> x
, sum(x, s(y)) -> s(sum(x, y))
, le(0(), x) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, take(0(), cons(y, ys)) -> y
, take(s(x), cons(y, ys)) -> take(x, ys)
, addList(x, y) ->
if(le(0(), min(len(x), len(y))), 0(), x, y, nil())
, if(false(), c, x, y, z) -> z
, if(true(), c, xs, ys, z) ->
if(le(s(c), min(len(xs), len(ys))),
s(c),
xs,
ys,
cons(sum(take(c, xs), take(c, ys)), z))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds