Problem AG01 3.5a

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AG01 3.5a

stdout:

MAYBE

Problem:
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
pred(s(x)) -> x
minus(x,0()) -> x
minus(x,s(y)) -> pred(minus(x,y))
mod(0(),y) -> 0()
mod(s(x),0()) -> 0()
mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
if_mod(false(),s(x),s(y)) -> s(x)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AG01 3.5a

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.5a

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)
     , pred(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> pred(minus(x, y))
     , mod(0(), y) -> 0()
     , mod(s(x), 0()) -> 0()
     , mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
     , if_mod(true(), s(x), s(y)) -> mod(minus(x, y), s(y))
     , if_mod(false(), s(x), s(y)) -> s(x)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	AG01 3.5a

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.5a

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)
     , pred(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> pred(minus(x, y))
     , mod(0(), y) -> 0()
     , mod(s(x), 0()) -> 0()
     , mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
     , if_mod(true(), s(x), s(y)) -> mod(minus(x, y), s(y))
     , if_mod(false(), s(x), s(y)) -> s(x)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool pair1rc

Execution Time	Unknown
Answer	TIMEOUT
Input	AG01 3.5a

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)
     , pred(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> pred(minus(x, y))
     , mod(0(), y) -> 0()
     , mod(s(x), 0()) -> 0()
     , mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
     , if_mod(true(), s(x), s(y)) -> mod(minus(x, y), s(y))
     , if_mod(false(), s(x), s(y)) -> s(x)}
  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 3.5a

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)
     , pred(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> pred(minus(x, y))
     , mod(0(), y) -> 0()
     , mod(s(x), 0()) -> 0()
     , mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
     , if_mod(true(), s(x), s(y)) -> mod(minus(x, y), s(y))
     , if_mod(false(), s(x), s(y)) -> s(x)}
  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 3.5a

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)
     , pred(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> pred(minus(x, y))
     , mod(0(), y) -> 0()
     , mod(s(x), 0()) -> 0()
     , mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
     , if_mod(true(), s(x), s(y)) -> mod(minus(x, y), s(y))
     , if_mod(false(), s(x), s(y)) -> s(x)}
  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 3.5a

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)
     , pred(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> pred(minus(x, y))
     , mod(0(), y) -> 0()
     , mod(s(x), 0()) -> 0()
     , mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
     , if_mod(true(), s(x), s(y)) -> mod(minus(x, y), s(y))
     , if_mod(false(), s(x), s(y)) -> s(x)}
  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 3.5a

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)
     , pred(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> pred(minus(x, y))
     , mod(0(), y) -> 0()
     , mod(s(x), 0()) -> 0()
     , mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
     , if_mod(true(), s(x), s(y)) -> mod(minus(x, y), s(y))
     , if_mod(false(), s(x), s(y)) -> s(x)}
  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	60.0647ms
Answer	TIMEOUT
Input	AG01 3.5a

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)
     , pred(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> pred(minus(x, y))
     , mod(0(), y) -> 0()
     , mod(s(x), 0()) -> 0()
     , mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
     , if_mod(true(), s(x), s(y)) -> mod(minus(x, y), s(y))
     , if_mod(false(), s(x), s(y)) -> s(x)}
  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..