Tool CaT
stdout:
MAYBE
Problem:
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
minus(x,x) -> 0()
minus(x,0()) -> x
minus(0(),x) -> 0()
minus(s(x),s(y)) -> minus(x,y)
isZero(0()) -> true()
isZero(s(x)) -> false()
mod(x,y) -> if_mod(isZero(y),le(y,x),x,y,minus(x,y))
if_mod(true(),b,x,y,z) -> divByZeroError()
if_mod(false(),false(),x,y,z) -> x
if_mod(false(),true(),x,y,z) -> mod(z,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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, x) -> 0()
, minus(x, 0()) -> x
, minus(0(), x) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, mod(x, y) -> if_mod(isZero(y), le(y, x), x, y, minus(x, y))
, if_mod(true(), b, x, y, z) -> divByZeroError()
, if_mod(false(), false(), x, y, z) -> x
, if_mod(false(), true(), x, y, z) -> mod(z, 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, x) -> 0()
, minus(x, 0()) -> x
, minus(0(), x) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, mod(x, y) -> if_mod(isZero(y), le(y, x), x, y, minus(x, y))
, if_mod(true(), b, x, y, z) -> divByZeroError()
, if_mod(false(), false(), x, y, z) -> x
, if_mod(false(), true(), x, y, z) -> mod(z, y)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds