Tool CaT
stdout:
MAYBE
Problem:
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
minus(x,0()) -> x
minus(0(),s(y)) -> 0()
minus(s(x),s(y)) -> minus(x,y)
plus(x,0()) -> x
plus(x,s(y)) -> s(plus(x,y))
mod(s(x),0()) -> 0()
mod(x,s(y)) -> help(x,s(y),0())
help(x,s(y),c) -> if(le(c,x),x,s(y),c)
if(true(),x,s(y),c) -> help(x,s(y),plus(c,s(y)))
if(false(),x,s(y),c) -> minus(x,minus(c,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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), s(y)) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, mod(s(x), 0()) -> 0()
, mod(x, s(y)) -> help(x, s(y), 0())
, help(x, s(y), c) -> if(le(c, x), x, s(y), c)
, if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y)))
, if(false(), x, s(y), c) -> minus(x, minus(c, 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, minus(x, 0()) -> x
, minus(0(), s(y)) -> 0()
, minus(s(x), s(y)) -> minus(x, y)
, plus(x, 0()) -> x
, plus(x, s(y)) -> s(plus(x, y))
, mod(s(x), 0()) -> 0()
, mod(x, s(y)) -> help(x, s(y), 0())
, help(x, s(y), c) -> if(le(c, x), x, s(y), c)
, if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y)))
, if(false(), x, s(y), c) -> minus(x, minus(c, s(y)))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds