Problem SK90 2.52

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	SK90 2.52

stdout:

MAYBE

Problem:
f(x,0(),0()) -> s(x)
f(0(),y,0()) -> s(y)
f(0(),0(),z) -> s(z)
f(s(0()),y,z) -> f(0(),s(y),s(z))
f(s(x),s(y),0()) -> f(x,y,s(0()))
f(s(x),0(),s(z)) -> f(x,s(0()),z)
f(0(),s(0()),s(0())) -> s(s(0()))
f(s(x),s(y),s(z)) -> f(x,y,f(s(x),s(y),z))
f(0(),s(s(y)),s(0())) -> f(0(),y,s(0()))
f(0(),s(0()),s(s(z))) -> f(0(),s(0()),z)
f(0(),s(s(y)),s(s(z))) -> f(0(),y,f(0(),s(s(y)),s(z)))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	SK90 2.52

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	SK90 2.52

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(x, 0(), 0()) -> s(x)
     , f(0(), y, 0()) -> s(y)
     , f(0(), 0(), z) -> s(z)
     , f(s(0()), y, z) -> f(0(), s(y), s(z))
     , f(s(x), s(y), 0()) -> f(x, y, s(0()))
     , f(s(x), 0(), s(z)) -> f(x, s(0()), z)
     , f(0(), s(0()), s(0())) -> s(s(0()))
     , f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
     , f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
     , f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
     , f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(z)))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	SK90 2.52

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	SK90 2.52

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  f(x, 0(), 0()) -> s(x)
     , f(0(), y, 0()) -> s(y)
     , f(0(), 0(), z) -> s(z)
     , f(s(0()), y, z) -> f(0(), s(y), s(z))
     , f(s(x), s(y), 0()) -> f(x, y, s(0()))
     , f(s(x), 0(), s(z)) -> f(x, s(0()), z)
     , f(0(), s(0()), s(0())) -> s(s(0()))
     , f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
     , f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
     , f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
     , f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(z)))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool pair2rc

Execution Time	Unknown
Answer	TIMEOUT
Input	SK90 2.52

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  f(x, 0(), 0()) -> s(x)
     , f(0(), y, 0()) -> s(y)
     , f(0(), 0(), z) -> s(z)
     , f(s(0()), y, z) -> f(0(), s(y), s(z))
     , f(s(x), s(y), 0()) -> f(x, y, s(0()))
     , f(s(x), 0(), s(z)) -> f(x, s(0()), z)
     , f(0(), s(0()), s(0())) -> s(s(0()))
     , f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
     , f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
     , f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
     , f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(z)))}
  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	SK90 2.52

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  f(x, 0(), 0()) -> s(x)
     , f(0(), y, 0()) -> s(y)
     , f(0(), 0(), z) -> s(z)
     , f(s(0()), y, z) -> f(0(), s(y), s(z))
     , f(s(x), s(y), 0()) -> f(x, y, s(0()))
     , f(s(x), 0(), s(z)) -> f(x, s(0()), z)
     , f(0(), s(0()), s(0())) -> s(s(0()))
     , f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
     , f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
     , f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
     , f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(z)))}
  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	SK90 2.52

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  f(x, 0(), 0()) -> s(x)
     , f(0(), y, 0()) -> s(y)
     , f(0(), 0(), z) -> s(z)
     , f(s(0()), y, z) -> f(0(), s(y), s(z))
     , f(s(x), s(y), 0()) -> f(x, y, s(0()))
     , f(s(x), 0(), s(z)) -> f(x, s(0()), z)
     , f(0(), s(0()), s(0())) -> s(s(0()))
     , f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
     , f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
     , f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
     , f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(z)))}
  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	MAYBE
Input	SK90 2.52

stdout:

MAYBE

We consider the following Problem:

  Strict Trs:
    {  f(x, 0(), 0()) -> s(x)
     , f(0(), y, 0()) -> s(y)
     , f(0(), 0(), z) -> s(z)
     , f(s(0()), y, z) -> f(0(), s(y), s(z))
     , f(s(x), s(y), 0()) -> f(x, y, s(0()))
     , f(s(x), 0(), s(z)) -> f(x, s(0()), z)
     , f(0(), s(0()), s(0())) -> s(s(0()))
     , f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
     , f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
     , f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
     , f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(z)))}
  StartTerms: basic terms
  Strategy: none

Certificate: MAYBE

Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
  None of the processors succeeded.

  Details of failed attempt(s):
  -----------------------------
    1) 'Fastest' failed due to the following reason:
         None of the processors succeeded.

         Details of failed attempt(s):
         -----------------------------
           1) 'Sequentially' failed due to the following reason:
                None of the processors succeeded.

                Details of failed attempt(s):
                -----------------------------
                  1) 'empty' failed due to the following reason:
                       Empty strict component of the problem is NOT empty.

                  2) 'Fastest' failed due to the following reason:
                       None of the processors succeeded.

                       Details of failed attempt(s):
                       -----------------------------
                         1) 'matrix-interpretation of dimension 3 (timeout of 100.0 seconds)' failed due to the following reason:
                              The input cannot be shown compatible

                         2) 'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' failed due to the following reason:
                              The input cannot be shown compatible



           2) 'Fastest' failed due to the following reason:
                None of the processors succeeded.

                Details of failed attempt(s):
                -----------------------------
                  1) 'Bounds with minimal-enrichment and initial automaton 'match' (timeout of 100.0 seconds)' failed due to the following reason:
                       match-boundness of the problem could not be verified.

                  2) 'Bounds with perSymbol-enrichment and initial automaton 'match' (timeout of 5.0 seconds)' failed due to the following reason:
                       match-boundness of the problem could not be verified.



    2) 'dp' failed due to the following reason:
         We have computed the following dependency pairs

         Strict Dependency Pairs:
           {  f^#(x, 0(), 0()) -> c_1(x)
            , f^#(0(), y, 0()) -> c_2(y)
            , f^#(0(), 0(), z) -> c_3(z)
            , f^#(s(0()), y, z) -> c_4(f^#(0(), s(y), s(z)))
            , f^#(s(x), s(y), 0()) -> c_5(f^#(x, y, s(0())))
            , f^#(s(x), 0(), s(z)) -> c_6(f^#(x, s(0()), z))
            , f^#(0(), s(0()), s(0())) -> c_7()
            , f^#(s(x), s(y), s(z)) -> c_8(f^#(x, y, f(s(x), s(y), z)))
            , f^#(0(), s(s(y)), s(0())) -> c_9(f^#(0(), y, s(0())))
            , f^#(0(), s(0()), s(s(z))) -> c_10(f^#(0(), s(0()), z))
            , f^#(0(), s(s(y)), s(s(z))) ->
              c_11(f^#(0(), y, f(0(), s(s(y)), s(z))))}

         We consider the following Problem:

           Strict DPs:
             {  f^#(x, 0(), 0()) -> c_1(x)
              , f^#(0(), y, 0()) -> c_2(y)
              , f^#(0(), 0(), z) -> c_3(z)
              , f^#(s(0()), y, z) -> c_4(f^#(0(), s(y), s(z)))
              , f^#(s(x), s(y), 0()) -> c_5(f^#(x, y, s(0())))
              , f^#(s(x), 0(), s(z)) -> c_6(f^#(x, s(0()), z))
              , f^#(0(), s(0()), s(0())) -> c_7()
              , f^#(s(x), s(y), s(z)) -> c_8(f^#(x, y, f(s(x), s(y), z)))
              , f^#(0(), s(s(y)), s(0())) -> c_9(f^#(0(), y, s(0())))
              , f^#(0(), s(0()), s(s(z))) -> c_10(f^#(0(), s(0()), z))
              , f^#(0(), s(s(y)), s(s(z))) ->
                c_11(f^#(0(), y, f(0(), s(s(y)), s(z))))}
           Strict Trs:
             {  f(x, 0(), 0()) -> s(x)
              , f(0(), y, 0()) -> s(y)
              , f(0(), 0(), z) -> s(z)
              , f(s(0()), y, z) -> f(0(), s(y), s(z))
              , f(s(x), s(y), 0()) -> f(x, y, s(0()))
              , f(s(x), 0(), s(z)) -> f(x, s(0()), z)
              , f(0(), s(0()), s(0())) -> s(s(0()))
              , f(s(x), s(y), s(z)) -> f(x, y, f(s(x), s(y), z))
              , f(0(), s(s(y)), s(0())) -> f(0(), y, s(0()))
              , f(0(), s(0()), s(s(z))) -> f(0(), s(0()), z)
              , f(0(), s(s(y)), s(s(z))) -> f(0(), y, f(0(), s(s(y)), s(z)))}
           StartTerms: basic terms
           Strategy: none

         Certificate: MAYBE

         Application of 'usablerules':
         -----------------------------
           All rules are usable.

           No subproblems were generated.


Arrrr..