Tool CaT
stdout:
MAYBE
Problem:
minus_active(0(),y) -> 0()
mark(0()) -> 0()
minus_active(s(x),s(y)) -> minus_active(x,y)
mark(s(x)) -> s(mark(x))
ge_active(x,0()) -> true()
mark(minus(x,y)) -> minus_active(x,y)
ge_active(0(),s(y)) -> false()
mark(ge(x,y)) -> ge_active(x,y)
ge_active(s(x),s(y)) -> ge_active(x,y)
mark(div(x,y)) -> div_active(mark(x),y)
div_active(0(),s(y)) -> 0()
mark(if(x,y,z)) -> if_active(mark(x),y,z)
div_active(s(x),s(y)) -> if_active(ge_active(x,y),s(div(minus(x,y),s(y))),0())
if_active(true(),x,y) -> mark(x)
minus_active(x,y) -> minus(x,y)
if_active(false(),x,y) -> mark(y)
ge_active(x,y) -> ge(x,y)
if_active(x,y,z) -> if(x,y,z)
div_active(x,y) -> div(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_active(0(), y) -> 0()
, mark(0()) -> 0()
, minus_active(s(x), s(y)) -> minus_active(x, y)
, mark(s(x)) -> s(mark(x))
, ge_active(x, 0()) -> true()
, mark(minus(x, y)) -> minus_active(x, y)
, ge_active(0(), s(y)) -> false()
, mark(ge(x, y)) -> ge_active(x, y)
, ge_active(s(x), s(y)) -> ge_active(x, y)
, mark(div(x, y)) -> div_active(mark(x), y)
, div_active(0(), s(y)) -> 0()
, mark(if(x, y, z)) -> if_active(mark(x), y, z)
, div_active(s(x), s(y)) ->
if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0())
, if_active(true(), x, y) -> mark(x)
, minus_active(x, y) -> minus(x, y)
, if_active(false(), x, y) -> mark(y)
, ge_active(x, y) -> ge(x, y)
, if_active(x, y, z) -> if(x, y, z)
, div_active(x, y) -> div(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_active(0(), y) -> 0()
, mark(0()) -> 0()
, minus_active(s(x), s(y)) -> minus_active(x, y)
, mark(s(x)) -> s(mark(x))
, ge_active(x, 0()) -> true()
, mark(minus(x, y)) -> minus_active(x, y)
, ge_active(0(), s(y)) -> false()
, mark(ge(x, y)) -> ge_active(x, y)
, ge_active(s(x), s(y)) -> ge_active(x, y)
, mark(div(x, y)) -> div_active(mark(x), y)
, div_active(0(), s(y)) -> 0()
, mark(if(x, y, z)) -> if_active(mark(x), y, z)
, div_active(s(x), s(y)) ->
if_active(ge_active(x, y), s(div(minus(x, y), s(y))), 0())
, if_active(true(), x, y) -> mark(x)
, minus_active(x, y) -> minus(x, y)
, if_active(false(), x, y) -> mark(y)
, ge_active(x, y) -> ge(x, y)
, if_active(x, y, z) -> if(x, y, z)
, div_active(x, y) -> div(x, y)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds