Tool CaT
stdout:
MAYBE
Problem:
double(x) -> permute(x,x,a())
permute(x,y,a()) -> permute(isZero(x),x,b())
permute(false(),x,b()) -> permute(ack(x,x),p(x),c())
permute(true(),x,b()) -> 0()
permute(y,x,c()) -> s(s(permute(x,y,a())))
p(0()) -> 0()
p(s(x)) -> x
ack(0(),x) -> plus(x,s(0()))
ack(s(x),0()) -> ack(x,s(0()))
ack(s(x),s(y)) -> ack(x,ack(s(x),y))
plus(0(),y) -> y
plus(s(x),y) -> plus(x,s(y))
plus(x,s(s(y))) -> s(plus(s(x),y))
plus(x,s(0())) -> s(x)
plus(x,0()) -> x
isZero(0()) -> true()
isZero(s(x)) -> false()
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:
{ double(x) -> permute(x, x, a())
, permute(x, y, a()) -> permute(isZero(x), x, b())
, permute(false(), x, b()) -> permute(ack(x, x), p(x), c())
, permute(true(), x, b()) -> 0()
, permute(y, x, c()) -> s(s(permute(x, y, a())))
, p(0()) -> 0()
, p(s(x)) -> x
, ack(0(), x) -> plus(x, s(0()))
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(x), y))
, plus(0(), y) -> y
, plus(s(x), y) -> plus(x, s(y))
, plus(x, s(s(y))) -> s(plus(s(x), y))
, plus(x, s(0())) -> s(x)
, plus(x, 0()) -> x
, isZero(0()) -> true()
, isZero(s(x)) -> false()}
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:
{ double(x) -> permute(x, x, a())
, permute(x, y, a()) -> permute(isZero(x), x, b())
, permute(false(), x, b()) -> permute(ack(x, x), p(x), c())
, permute(true(), x, b()) -> 0()
, permute(y, x, c()) -> s(s(permute(x, y, a())))
, p(0()) -> 0()
, p(s(x)) -> x
, ack(0(), x) -> plus(x, s(0()))
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(x), y))
, plus(0(), y) -> y
, plus(s(x), y) -> plus(x, s(y))
, plus(x, s(s(y))) -> s(plus(s(x), y))
, plus(x, s(0())) -> s(x)
, plus(x, 0()) -> x
, isZero(0()) -> true()
, isZero(s(x)) -> false()}
Proof Output:
Computation stopped due to timeout after 60.0 seconds