Tool CaT
stdout:
MAYBE
Problem:
+(0(),y) -> y
+(s(x),y) -> s(+(x,y))
++(nil(),ys) -> ys
++(:(x,xs),ys) -> :(x,++(xs,ys))
sum(:(x,nil())) -> :(x,nil())
sum(:(x,:(y,xs))) -> sum(:(+(x,y),xs))
sum(++(xs,:(x,:(y,ys)))) -> sum(++(xs,sum(:(x,:(y,ys)))))
-(x,0()) -> x
-(0(),s(y)) -> 0()
-(s(x),s(y)) -> -(x,y)
quot(0(),s(y)) -> 0()
quot(s(x),s(y)) -> s(quot(-(x,y),s(y)))
length(nil()) -> 0()
length(:(x,xs)) -> s(length(xs))
hd(:(x,xs)) -> x
avg(xs) -> quot(hd(sum(xs)),length(xs))
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:
{ +(0(), y) -> y
, +(s(x), y) -> s(+(x, y))
, ++(nil(), ys) -> ys
, ++(:(x, xs), ys) -> :(x, ++(xs, ys))
, sum(:(x, nil())) -> :(x, nil())
, sum(:(x, :(y, xs))) -> sum(:(+(x, y), xs))
, sum(++(xs, :(x, :(y, ys)))) -> sum(++(xs, sum(:(x, :(y, ys)))))
, -(x, 0()) -> x
, -(0(), s(y)) -> 0()
, -(s(x), s(y)) -> -(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(-(x, y), s(y)))
, length(nil()) -> 0()
, length(:(x, xs)) -> s(length(xs))
, hd(:(x, xs)) -> x
, avg(xs) -> quot(hd(sum(xs)), length(xs))}
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:
{ +(0(), y) -> y
, +(s(x), y) -> s(+(x, y))
, ++(nil(), ys) -> ys
, ++(:(x, xs), ys) -> :(x, ++(xs, ys))
, sum(:(x, nil())) -> :(x, nil())
, sum(:(x, :(y, xs))) -> sum(:(+(x, y), xs))
, sum(++(xs, :(x, :(y, ys)))) -> sum(++(xs, sum(:(x, :(y, ys)))))
, -(x, 0()) -> x
, -(0(), s(y)) -> 0()
, -(s(x), s(y)) -> -(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(-(x, y), s(y)))
, length(nil()) -> 0()
, length(:(x, xs)) -> s(length(xs))
, hd(:(x, xs)) -> x
, avg(xs) -> quot(hd(sum(xs)), length(xs))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds