Problem SK90 4.54

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	SK90 4.54

stdout:

MAYBE

Problem:
g(f(x,y)) -> f(f(g(g(x)),g(g(y))),f(g(g(x)),g(g(y))))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	SK90 4.54

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	MAYBE
Input	SK90 4.54

stdout:

MAYBE

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

Proof Output:
  None of the processors succeeded.

  Details of failed attempt(s):
  -----------------------------
    1) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:

             {1: g^#(f(x, y)) ->
                 c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{1}                                                       [         NA         ]



         Sub-problems:
         -------------
           * Path {1}: NA
             ------------

             The usable rules for this path are:

               {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE

             We have not generated a proof for the resulting sub-problem.

    2) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:

             {1: g^#(f(x, y)) ->
                 c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{1}                                                       [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------

             The usable rules for this path are:

               {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE

             We apply the sub-processor on the resulting sub-problem:

             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost runtime-complexity with respect to
               Rules:
                 {  g^#(f(x, y)) -> c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))
                  , g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             Proof Output:
               The input cannot be shown compatible

    3) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:

             {1: g^#(f(x, y)) ->
                 c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{1}                                                       [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------

             The usable rules for this path are:

               {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE

             We apply the sub-processor on the resulting sub-problem:

             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost runtime-complexity with respect to
               Rules:
                 {  g^#(f(x, y)) -> c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))
                  , g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             Proof Output:
               The input cannot be shown compatible

    4) 'matrix-interpretation of dimension 1' failed due to the following reason:
         The input cannot be shown compatible

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

    6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	SK90 4.54

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	MAYBE
Input	SK90 4.54

stdout:

MAYBE

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

Proof Output:
  None of the processors succeeded.

  Details of failed attempt(s):
  -----------------------------
    1) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:

             {1: g^#(f(x, y)) ->
                 c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{1}                                                       [         NA         ]



         Sub-problems:
         -------------
           * Path {1}: NA
             ------------

             The usable rules for this path are:

               {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE

             We have not generated a proof for the resulting sub-problem.

    2) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:

             {1: g^#(f(x, y)) ->
                 c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{1}                                                       [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------

             The usable rules for this path are:

               {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE

             We apply the sub-processor on the resulting sub-problem:

             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    runtime-complexity with respect to
               Rules:
                 {  g^#(f(x, y)) -> c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))
                  , g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             Proof Output:
               The input cannot be shown compatible

    3) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:

             {1: g^#(f(x, y)) ->
                 c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))}

           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)

             ->{1}                                                       [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1}: MAYBE
             ---------------

             The usable rules for this path are:

               {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             The weight gap principle does not apply:
               The input cannot be shown compatible
             Complexity induced by the adequate RMI: MAYBE

             We apply the sub-processor on the resulting sub-problem:

             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    runtime-complexity with respect to
               Rules:
                 {  g^#(f(x, y)) -> c_0(g^#(g(x)), g^#(g(y)), g^#(g(x)), g^#(g(y)))
                  , g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}

             Proof Output:
               The input cannot be shown compatible

    4) 'matrix-interpretation of dimension 1' failed due to the following reason:
         The input cannot be shown compatible

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

    6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
         match-boundness of the problem could not be verified.

Tool pair2rc

Execution Time	Unknown
Answer	TIMEOUT
Input	SK90 4.54

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}
  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 4.54

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}
  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 4.54

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}
  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	SK90 4.54

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}
  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	61.012188ms
Answer	TIMEOUT
Input	SK90 4.54

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))}
  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..