Problem AProVE 10 Zantema06-03-modified

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 10 Zantema06-03-modified

stdout:

MAYBE

Problem:
a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
a(c(x)) -> c(a(x))
c(b(x)) -> b(c(x))
dup(A'(a(b(b(x))))) -> collapse(A'(a(x)),A'(a(x)))
collapse(x,y) -> dup(x)
collapse(x,y) -> dup(y)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 10 Zantema06-03-modified

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 10 Zantema06-03-modified

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
     , a(c(x)) -> c(a(x))
     , c(b(x)) -> b(c(x))
     , dup(A'(a(b(b(x))))) -> collapse(A'(a(x)), A'(a(x)))
     , collapse(x, y) -> dup(x)
     , collapse(x, y) -> dup(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: a^#(a(b(b(x)))) -> c_0(a^#(a(a(x))))
              , 2: a^#(c(x)) -> c_1(c^#(a(x)))
              , 3: c^#(b(x)) -> c_2(c^#(x))
              , 4: dup^#(A'(a(b(b(x))))) -> c_3(collapse^#(A'(a(x)), A'(a(x))))
              , 5: collapse^#(x, y) -> c_4(dup^#(x))
              , 6: collapse^#(x, y) -> c_5(dup^#(y))}

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

             ->{4,6,5}                                                   [         NA         ]

             ->{1}                                                       [     inherited      ]
                |
                `->{2}                                                   [     inherited      ]
                    |
                    `->{3}                                               [       MAYBE        ]



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

             This path is subsumed by the proof of path {1}->{2}->{3}.

           * Path {1}->{2}: inherited
             ------------------------

             This path is subsumed by the proof of path {1}->{2}->{3}.

           * Path {1}->{2}->{3}: MAYBE
             -------------------------

             The usable rules for this path are:

               {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                , a(c(x)) -> c(a(x))
                , c(b(x)) -> b(c(x))}

             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:
                 {  a^#(c(x)) -> c_1(c^#(a(x)))
                  , a^#(a(b(b(x)))) -> c_0(a^#(a(a(x))))
                  , c^#(b(x)) -> c_2(c^#(x))
                  , a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                  , a(c(x)) -> c(a(x))
                  , c(b(x)) -> b(c(x))}

             Proof Output:
               The input cannot be shown compatible

           * Path {4,6,5}: NA
             ----------------

             The usable rules for this path are:

               {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                , a(c(x)) -> c(a(x))
                , c(b(x)) -> b(c(x))}

             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: a^#(a(b(b(x)))) -> c_0(a^#(a(a(x))))
              , 2: a^#(c(x)) -> c_1(c^#(a(x)))
              , 3: c^#(b(x)) -> c_2(c^#(x))
              , 4: dup^#(A'(a(b(b(x))))) -> c_3(collapse^#(A'(a(x)), A'(a(x))))
              , 5: collapse^#(x, y) -> c_4(dup^#(x))
              , 6: collapse^#(x, y) -> c_5(dup^#(y))}

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

             ->{4,6,5}                                                   [         NA         ]

             ->{1}                                                       [     inherited      ]
                |
                `->{2}                                                   [     inherited      ]
                    |
                    `->{3}                                               [       MAYBE        ]



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

             This path is subsumed by the proof of path {1}->{2}->{3}.

           * Path {1}->{2}: inherited
             ------------------------

             This path is subsumed by the proof of path {1}->{2}->{3}.

           * Path {1}->{2}->{3}: MAYBE
             -------------------------

             The usable rules for this path are:

               {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                , a(c(x)) -> c(a(x))
                , c(b(x)) -> b(c(x))}

             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:
                 {  a^#(c(x)) -> c_1(c^#(a(x)))
                  , a^#(a(b(b(x)))) -> c_0(a^#(a(a(x))))
                  , c^#(b(x)) -> c_2(c^#(x))
                  , a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                  , a(c(x)) -> c(a(x))
                  , c(b(x)) -> b(c(x))}

             Proof Output:
               The input cannot be shown compatible

           * Path {4,6,5}: NA
             ----------------

             The usable rules for this path are:

               {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                , a(c(x)) -> c(a(x))
                , c(b(x)) -> b(c(x))}

             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.

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

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

    5) '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	AProVE 10 Zantema06-03-modified

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	MAYBE
Input	AProVE 10 Zantema06-03-modified

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
     , a(c(x)) -> c(a(x))
     , c(b(x)) -> b(c(x))
     , dup(A'(a(b(b(x))))) -> collapse(A'(a(x)), A'(a(x)))
     , collapse(x, y) -> dup(x)
     , collapse(x, y) -> dup(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: a^#(a(b(b(x)))) -> c_0(a^#(a(a(x))))
              , 2: a^#(c(x)) -> c_1(c^#(a(x)))
              , 3: c^#(b(x)) -> c_2(c^#(x))
              , 4: dup^#(A'(a(b(b(x))))) -> c_3(collapse^#(A'(a(x)), A'(a(x))))
              , 5: collapse^#(x, y) -> c_4(dup^#(x))
              , 6: collapse^#(x, y) -> c_5(dup^#(y))}

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

             ->{4,6,5}                                                   [         NA         ]

             ->{1}                                                       [     inherited      ]
                |
                `->{2}                                                   [     inherited      ]
                    |
                    `->{3}                                               [       MAYBE        ]



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

             This path is subsumed by the proof of path {1}->{2}->{3}.

           * Path {1}->{2}: inherited
             ------------------------

             This path is subsumed by the proof of path {1}->{2}->{3}.

           * Path {1}->{2}->{3}: MAYBE
             -------------------------

             The usable rules for this path are:

               {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                , a(c(x)) -> c(a(x))
                , c(b(x)) -> b(c(x))}

             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:
                 {  a^#(c(x)) -> c_1(c^#(a(x)))
                  , a^#(a(b(b(x)))) -> c_0(a^#(a(a(x))))
                  , c^#(b(x)) -> c_2(c^#(x))
                  , a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                  , a(c(x)) -> c(a(x))
                  , c(b(x)) -> b(c(x))}

             Proof Output:
               The input cannot be shown compatible

           * Path {4,6,5}: NA
             ----------------

             The usable rules for this path are:

               {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                , a(c(x)) -> c(a(x))
                , c(b(x)) -> b(c(x))}

             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: a^#(a(b(b(x)))) -> c_0(a^#(a(a(x))))
              , 2: a^#(c(x)) -> c_1(c^#(a(x)))
              , 3: c^#(b(x)) -> c_2(c^#(x))
              , 4: dup^#(A'(a(b(b(x))))) -> c_3(collapse^#(A'(a(x)), A'(a(x))))
              , 5: collapse^#(x, y) -> c_4(dup^#(x))
              , 6: collapse^#(x, y) -> c_5(dup^#(y))}

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

             ->{4,6,5}                                                   [         NA         ]

             ->{1}                                                       [     inherited      ]
                |
                `->{2}                                                   [     inherited      ]
                    |
                    `->{3}                                               [       MAYBE        ]



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

             This path is subsumed by the proof of path {1}->{2}->{3}.

           * Path {1}->{2}: inherited
             ------------------------

             This path is subsumed by the proof of path {1}->{2}->{3}.

           * Path {1}->{2}->{3}: MAYBE
             -------------------------

             The usable rules for this path are:

               {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                , a(c(x)) -> c(a(x))
                , c(b(x)) -> b(c(x))}

             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:
                 {  a^#(c(x)) -> c_1(c^#(a(x)))
                  , a^#(a(b(b(x)))) -> c_0(a^#(a(a(x))))
                  , c^#(b(x)) -> c_2(c^#(x))
                  , a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                  , a(c(x)) -> c(a(x))
                  , c(b(x)) -> b(c(x))}

             Proof Output:
               The input cannot be shown compatible

           * Path {4,6,5}: NA
             ----------------

             The usable rules for this path are:

               {  a(a(b(b(x)))) -> b(b(b(a(a(a(x))))))
                , a(c(x)) -> c(a(x))
                , c(b(x)) -> b(c(x))}

             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.

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

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

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