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