Problem AG01 3.40

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AG01 3.40

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)))
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AG01 3.40

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.40

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)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , plus(minus(x, s(0())), minus(y, s(s(z)))) ->
       plus(minus(y, s(s(z))), minus(x, s(0())))
     , plus(plus(x, s(0())), plus(y, s(s(z)))) ->
       plus(plus(y, s(s(z))), plus(x, s(0())))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AG01 3.40

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.40

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)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , plus(minus(x, s(0())), minus(y, s(s(z)))) ->
       plus(minus(y, s(s(z))), minus(x, s(0())))
     , plus(plus(x, s(0())), plus(y, s(s(z)))) ->
       plus(plus(y, s(s(z))), plus(x, s(0())))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool pair1rc

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.40

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  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)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , plus(minus(x, s(0())), minus(y, s(s(z)))) ->
       plus(minus(y, s(s(z))), minus(x, s(0())))
     , plus(plus(x, s(0())), plus(y, s(s(z)))) ->
       plus(plus(y, s(s(z))), plus(x, 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 3.40

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  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)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , plus(minus(x, s(0())), minus(y, s(s(z)))) ->
       plus(minus(y, s(s(z))), minus(x, s(0())))
     , plus(plus(x, s(0())), plus(y, s(s(z)))) ->
       plus(plus(y, s(s(z))), plus(x, 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 3.40

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  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)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , plus(minus(x, s(0())), minus(y, s(s(z)))) ->
       plus(minus(y, s(s(z))), minus(x, s(0())))
     , plus(plus(x, s(0())), plus(y, s(s(z)))) ->
       plus(plus(y, s(s(z))), plus(x, 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 3.40

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  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)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , plus(minus(x, s(0())), minus(y, s(s(z)))) ->
       plus(minus(y, s(s(z))), minus(x, s(0())))
     , plus(plus(x, s(0())), plus(y, s(s(z)))) ->
       plus(plus(y, s(s(z))), plus(x, 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 3.40

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  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)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , plus(minus(x, s(0())), minus(y, s(s(z)))) ->
       plus(minus(y, s(s(z))), minus(x, s(0())))
     , plus(plus(x, s(0())), plus(y, s(s(z)))) ->
       plus(plus(y, s(s(z))), plus(x, 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	60.06112ms
Answer	TIMEOUT
Input	AG01 3.40

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  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)))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , plus(minus(x, s(0())), minus(y, s(s(z)))) ->
       plus(minus(y, s(s(z))), minus(x, s(0())))
     , plus(plus(x, s(0())), plus(y, s(s(z)))) ->
       plus(plus(y, s(s(z))), plus(x, 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..