Tool CaT
stdout:
MAYBE
Problem:
minus(s(x),y) -> if(gt(s(x),y),x,y)
if(true(),x,y) -> s(minus(x,y))
if(false(),x,y) -> 0()
gcd(x,y) -> if1(ge(x,y),x,y)
if1(true(),x,y) -> if2(gt(y,0()),x,y)
if1(false(),x,y) -> if3(gt(x,0()),x,y)
if2(true(),x,y) -> gcd(minus(x,y),y)
if2(false(),x,y) -> x
if3(true(),x,y) -> gcd(x,minus(y,x))
if3(false(),x,y) -> y
gt(0(),y) -> false()
gt(s(x),0()) -> true()
gt(s(x),s(y)) -> gt(x,y)
ge(x,0()) -> true()
ge(0(),s(x)) -> false()
ge(s(x),s(y)) -> ge(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(s(x), y) -> if(gt(s(x), y), x, y)
, if(true(), x, y) -> s(minus(x, y))
, if(false(), x, y) -> 0()
, gcd(x, y) -> if1(ge(x, y), x, y)
, if1(true(), x, y) -> if2(gt(y, 0()), x, y)
, if1(false(), x, y) -> if3(gt(x, 0()), x, y)
, if2(true(), x, y) -> gcd(minus(x, y), y)
, if2(false(), x, y) -> x
, if3(true(), x, y) -> gcd(x, minus(y, x))
, if3(false(), x, y) -> y
, gt(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(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(s(x), y) -> if(gt(s(x), y), x, y)
, if(true(), x, y) -> s(minus(x, y))
, if(false(), x, y) -> 0()
, gcd(x, y) -> if1(ge(x, y), x, y)
, if1(true(), x, y) -> if2(gt(y, 0()), x, y)
, if1(false(), x, y) -> if3(gt(x, 0()), x, y)
, if2(true(), x, y) -> gcd(minus(x, y), y)
, if2(false(), x, y) -> x
, if3(true(), x, y) -> gcd(x, minus(y, x))
, if3(false(), x, y) -> y
, gt(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, ge(x, 0()) -> true()
, ge(0(), s(x)) -> false()
, ge(s(x), s(y)) -> ge(x, y)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds