Tool CaT
stdout:
MAYBE
Problem:
gt(s(x),0()) -> true()
gt(0(),y) -> false()
gt(s(x),s(y)) -> gt(x,y)
divides(x,y) -> div(x,y,y)
div(0(),0(),z) -> true()
div(0(),s(x),z) -> false()
div(s(x),0(),s(z)) -> div(s(x),s(z),s(z))
div(s(x),s(y),z) -> div(x,y,z)
prime(x) -> test(x,s(s(0())))
test(x,y) -> if1(gt(x,y),x,y)
if1(true(),x,y) -> if2(divides(x,y),x,y)
if1(false(),x,y) -> true()
if2(true(),x,y) -> false()
if2(false(),x,y) -> test(x,s(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:
{ gt(s(x), 0()) -> true()
, gt(0(), y) -> false()
, gt(s(x), s(y)) -> gt(x, y)
, divides(x, y) -> div(x, y, y)
, div(0(), 0(), z) -> true()
, div(0(), s(x), z) -> false()
, div(s(x), 0(), s(z)) -> div(s(x), s(z), s(z))
, div(s(x), s(y), z) -> div(x, y, z)
, prime(x) -> test(x, s(s(0())))
, test(x, y) -> if1(gt(x, y), x, y)
, if1(true(), x, y) -> if2(divides(x, y), x, y)
, if1(false(), x, y) -> true()
, if2(true(), x, y) -> false()
, if2(false(), x, y) -> test(x, s(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:
{ gt(s(x), 0()) -> true()
, gt(0(), y) -> false()
, gt(s(x), s(y)) -> gt(x, y)
, divides(x, y) -> div(x, y, y)
, div(0(), 0(), z) -> true()
, div(0(), s(x), z) -> false()
, div(s(x), 0(), s(z)) -> div(s(x), s(z), s(z))
, div(s(x), s(y), z) -> div(x, y, z)
, prime(x) -> test(x, s(s(0())))
, test(x, y) -> if1(gt(x, y), x, y)
, if1(true(), x, y) -> if2(divides(x, y), x, y)
, if1(false(), x, y) -> true()
, if2(true(), x, y) -> false()
, if2(false(), x, y) -> test(x, s(y))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds