Tool CaT
stdout:
MAYBE
Problem:
gt(0(),y) -> false()
gt(s(x),0()) -> true()
gt(s(x),s(y)) -> gt(x,y)
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
average(x,y) -> aver(plus(x,y),0())
aver(sum,z) -> if(gt(sum,double(z)),sum,z)
if(true(),sum,z) -> aver(sum,s(z))
if(false(),sum,z) -> z
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(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, average(x, y) -> aver(plus(x, y), 0())
, aver(sum, z) -> if(gt(sum, double(z)), sum, z)
, if(true(), sum, z) -> aver(sum, s(z))
, if(false(), sum, z) -> z}
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(0(), y) -> false()
, gt(s(x), 0()) -> true()
, gt(s(x), s(y)) -> gt(x, y)
, plus(0(), y) -> y
, plus(s(x), y) -> s(plus(x, y))
, double(0()) -> 0()
, double(s(x)) -> s(s(double(x)))
, average(x, y) -> aver(plus(x, y), 0())
, aver(sum, z) -> if(gt(sum, double(z)), sum, z)
, if(true(), sum, z) -> aver(sum, s(z))
, if(false(), sum, z) -> z}
Proof Output:
Computation stopped due to timeout after 60.0 seconds