Problem AProVE 06 logarithm

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 06 logarithm

stdout:

MAYBE

Problem:
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)))
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
inc(s(x)) -> s(inc(x))
inc(0()) -> s(0())
log(x) -> logIter(x,0())
logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),quot(x,s(s(0()))),inc(y))
if(false(),b,x,y) -> logZeroError()
if(true(),false(),x,s(y)) -> y
if(true(),true(),x,y) -> logIter(x,y)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 06 logarithm

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 06 logarithm

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  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)))
     , le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , log(x) -> logIter(x, 0())
     , logIter(x, y) ->
       if(le(s(0()), x), le(s(s(0())), x), quot(x, s(s(0()))), inc(y))
     , if(false(), b, x, y) -> logZeroError()
     , if(true(), false(), x, s(y)) -> y
     , if(true(), true(), x, y) -> logIter(x, y)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 06 logarithm

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AProVE 06 logarithm

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  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)))
     , le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , log(x) -> logIter(x, 0())
     , logIter(x, y) ->
       if(le(s(0()), x), le(s(s(0())), x), quot(x, s(s(0()))), inc(y))
     , if(false(), b, x, y) -> logZeroError()
     , if(true(), false(), x, s(y)) -> y
     , if(true(), true(), x, y) -> logIter(x, y)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds