Tool CaT
stdout:
MAYBE
Problem:
minus(minus(x,y),z) -> minus(x,plus(y,z))
minus(0(),y) -> 0()
minus(x,0()) -> x
minus(s(x),s(y)) -> minus(x,y)
plus(0(),y) -> y
plus(s(x),y) -> plus(x,s(y))
plus(s(x),y) -> s(plus(y,x))
zero(s(x)) -> false()
zero(0()) -> true()
p(s(x)) -> x
p(0()) -> 0()
div(x,y) -> quot(x,y,0())
quot(s(x),s(y),z) -> quot(minus(p(ack(0(),x)),y),s(y),s(z))
quot(0(),s(y),z) -> z
ack(0(),x) -> s(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))
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:
{ minus(minus(x, y), z) -> minus(x, plus(y, z))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), y) -> y
, plus(s(x), y) -> plus(x, s(y))
, plus(s(x), y) -> s(plus(y, x))
, zero(s(x)) -> false()
, zero(0()) -> true()
, p(s(x)) -> x
, p(0()) -> 0()
, div(x, y) -> quot(x, y, 0())
, quot(s(x), s(y), z) -> quot(minus(p(ack(0(), x)), y), s(y), s(z))
, quot(0(), s(y), z) -> z
, ack(0(), x) -> s(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))}
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:
{ minus(minus(x, y), z) -> minus(x, plus(y, z))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), y) -> y
, plus(s(x), y) -> plus(x, s(y))
, plus(s(x), y) -> s(plus(y, x))
, zero(s(x)) -> false()
, zero(0()) -> true()
, p(s(x)) -> x
, p(0()) -> 0()
, div(x, y) -> quot(x, y, 0())
, quot(s(x), s(y), z) -> quot(minus(p(ack(0(), x)), y), s(y), s(z))
, quot(0(), s(y), z) -> z
, ack(0(), x) -> s(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))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds