Problem AG01 3.8b

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AG01 3.8b

stdout:

MAYBE

Problem:
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
minus(0(),y) -> 0()
minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
if_minus(true(),s(x),y) -> 0()
if_minus(false(),s(x),y) -> s(minus(x,y))
quot(0(),s(y)) -> 0()
quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
log(s(0())) -> 0()
log(s(s(x))) -> s(log(s(quot(x,s(s(0()))))))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AG01 3.8b

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.8b

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(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , quot(0(), s(y)) -> 0()
     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
     , log(s(0())) -> 0()
     , log(s(s(x))) -> s(log(s(quot(x, s(s(0()))))))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AG01 3.8b

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.8b

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(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , quot(0(), s(y)) -> 0()
     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
     , log(s(0())) -> 0()
     , log(s(s(x))) -> s(log(s(quot(x, s(s(0()))))))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool pair1rc

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.8b

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , quot(0(), s(y)) -> 0()
     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
     , log(s(0())) -> 0()
     , log(s(s(x))) -> s(log(s(quot(x, s(s(0()))))))}
  StartTerms: basic terms
  Strategy: none

Certificate: TIMEOUT

Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool pair2rc

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.8b

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , quot(0(), s(y)) -> 0()
     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
     , log(s(0())) -> 0()
     , log(s(s(x))) -> s(log(s(quot(x, s(s(0()))))))}
  StartTerms: basic terms
  Strategy: none

Certificate: TIMEOUT

Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool pair3irc

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.8b

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , quot(0(), s(y)) -> 0()
     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
     , log(s(0())) -> 0()
     , log(s(s(x))) -> s(log(s(quot(x, s(s(0()))))))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: TIMEOUT

Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool pair3rc

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.8b

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , quot(0(), s(y)) -> 0()
     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
     , log(s(0())) -> 0()
     , log(s(s(x))) -> s(log(s(quot(x, s(s(0()))))))}
  StartTerms: basic terms
  Strategy: none

Certificate: TIMEOUT

Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool rc

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.8b

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , quot(0(), s(y)) -> 0()
     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
     , log(s(0())) -> 0()
     , log(s(s(x))) -> s(log(s(quot(x, s(s(0()))))))}
  StartTerms: basic terms
  Strategy: none

Certificate: TIMEOUT

Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..

Tool tup3irc

Execution Time	60.070053ms
Answer	TIMEOUT
Input	AG01 3.8b

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , quot(0(), s(y)) -> 0()
     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
     , log(s(0())) -> 0()
     , log(s(s(x))) -> s(log(s(quot(x, s(s(0()))))))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: TIMEOUT

Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
  Computation stopped due to timeout after 60.0 seconds

Arrrr..