Tool CaT
stdout:
MAYBE
Problem:
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
inc(0()) -> 0()
inc(s(x)) -> s(inc(x))
minus(0(),y) -> 0()
minus(x,0()) -> x
minus(s(x),s(y)) -> minus(x,y)
quot(0(),s(y)) -> 0()
quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
log(x) -> log2(x,0())
log2(x,y) -> if(le(x,0()),le(x,s(0())),x,inc(y))
if(true(),b,x,y) -> log_undefined()
if(false(),b,x,y) -> if2(b,x,y)
if2(true(),x,s(y)) -> y
if2(false(),x,y) -> log2(quot(x,s(s(0()))),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)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, 0()), le(x, s(0())), x, inc(y))
, if(true(), b, x, y) -> log_undefined()
, if(false(), b, x, y) -> if2(b, x, y)
, if2(true(), x, s(y)) -> y
, if2(false(), x, y) -> log2(quot(x, s(s(0()))), 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)
, inc(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, minus(0(), y) -> 0()
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, quot(0(), s(y)) -> 0()
, quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
, log(x) -> log2(x, 0())
, log2(x, y) -> if(le(x, 0()), le(x, s(0())), x, inc(y))
, if(true(), b, x, y) -> log_undefined()
, if(false(), b, x, y) -> if2(b, x, y)
, if2(true(), x, s(y)) -> y
, if2(false(), x, y) -> log2(quot(x, s(s(0()))), y)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds