Problem Transformed outermost 08 cariboo ex2

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed outermost 08 cariboo ex2

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	MAYBE
Input	Transformed outermost 08 cariboo ex2

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  cons_1(x, cons_1(y, z)) -> big_0()
     , cons_1(x, cons_0(y, z)) -> big_0()
     , *top*_0(inf_1(x)) -> *top*_0(cons_0(x, inf_1(s_0(x))))
     , s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
     , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
     , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))}

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: cons_1^#(x, cons_1(y, z)) -> c_0()
              , 2: cons_1^#(x, cons_0(y, z)) -> c_1()
              , 3: *top*_0^#(inf_1(x)) ->
                   c_2(*top*_0^#(cons_0(x, inf_1(s_0(x)))))
              , 4: s_0^#(inf_1(x)) -> c_3(s_0^#(cons_0(x, inf_1(s_0(x)))))
              , 5: cons_0^#(inf_1(x), x0) ->
                   c_4(cons_0^#(cons_0(x, inf_1(s_0(x))), x0))
              , 6: cons_0^#(x0, inf_1(x)) ->
                   c_5(cons_1^#(x0, cons_0(x, inf_1(s_0(x)))))}

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

             ->{5}                                                       [     inherited      ]
                |
                `->{6}                                                   [     inherited      ]
                    |
                    |->{1}                                               [         NA         ]
                    |
                    `->{2}                                               [         NA         ]

             ->{4}                                                       [       MAYBE        ]

             ->{3}                                                       [         NA         ]



         Sub-problems:
         -------------
           * Path {3}: NA
             ------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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.

           * Path {4}: MAYBE
             ---------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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:
                 {  s_0^#(inf_1(x)) -> c_3(s_0^#(cons_0(x, inf_1(s_0(x)))))
                  , s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                  , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                  , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                  , cons_1(x, cons_1(y, z)) -> big_0()
                  , cons_1(x, cons_0(y, z)) -> big_0()}

             Proof Output:
               The input cannot be shown compatible

           * Path {5}: inherited
             -------------------

             This path is subsumed by the proof of path {5}->{6}->{1}.

           * Path {5}->{6}: inherited
             ------------------------

             This path is subsumed by the proof of path {5}->{6}->{1}.

           * Path {5}->{6}->{1}: NA
             ----------------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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.

           * Path {5}->{6}->{2}: NA
             ----------------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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: cons_1^#(x, cons_1(y, z)) -> c_0()
              , 2: cons_1^#(x, cons_0(y, z)) -> c_1()
              , 3: *top*_0^#(inf_1(x)) ->
                   c_2(*top*_0^#(cons_0(x, inf_1(s_0(x)))))
              , 4: s_0^#(inf_1(x)) -> c_3(s_0^#(cons_0(x, inf_1(s_0(x)))))
              , 5: cons_0^#(inf_1(x), x0) ->
                   c_4(cons_0^#(cons_0(x, inf_1(s_0(x))), x0))
              , 6: cons_0^#(x0, inf_1(x)) ->
                   c_5(cons_1^#(x0, cons_0(x, inf_1(s_0(x)))))}

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

             ->{5}                                                       [     inherited      ]
                |
                `->{6}                                                   [     inherited      ]
                    |
                    |->{1}                                               [         NA         ]
                    |
                    `->{2}                                               [         NA         ]

             ->{4}                                                       [       MAYBE        ]

             ->{3}                                                       [         NA         ]



         Sub-problems:
         -------------
           * Path {3}: NA
             ------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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.

           * Path {4}: MAYBE
             ---------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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:
                 {  s_0^#(inf_1(x)) -> c_3(s_0^#(cons_0(x, inf_1(s_0(x)))))
                  , s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                  , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                  , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                  , cons_1(x, cons_1(y, z)) -> big_0()
                  , cons_1(x, cons_0(y, z)) -> big_0()}

             Proof Output:
               The input cannot be shown compatible

           * Path {5}: inherited
             -------------------

             This path is subsumed by the proof of path {5}->{6}->{1}.

           * Path {5}->{6}: inherited
             ------------------------

             This path is subsumed by the proof of path {5}->{6}->{1}.

           * Path {5}->{6}->{1}: NA
             ----------------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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.

           * Path {5}->{6}->{2}: NA
             ----------------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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	Transformed outermost 08 cariboo ex2

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	MAYBE
Input	Transformed outermost 08 cariboo ex2

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    runtime-complexity with respect to
  Rules:
    {  cons_1(x, cons_1(y, z)) -> big_0()
     , cons_1(x, cons_0(y, z)) -> big_0()
     , *top*_0(inf_1(x)) -> *top*_0(cons_0(x, inf_1(s_0(x))))
     , s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
     , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
     , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))}

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: cons_1^#(x, cons_1(y, z)) -> c_0()
              , 2: cons_1^#(x, cons_0(y, z)) -> c_1()
              , 3: *top*_0^#(inf_1(x)) ->
                   c_2(*top*_0^#(cons_0(x, inf_1(s_0(x)))))
              , 4: s_0^#(inf_1(x)) -> c_3(s_0^#(cons_0(x, inf_1(s_0(x)))))
              , 5: cons_0^#(inf_1(x), x0) ->
                   c_4(cons_0^#(cons_0(x, inf_1(s_0(x))), x0))
              , 6: cons_0^#(x0, inf_1(x)) ->
                   c_5(cons_1^#(x0, cons_0(x, inf_1(s_0(x)))))}

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

             ->{5}                                                       [     inherited      ]
                |
                `->{6}                                                   [     inherited      ]
                    |
                    |->{1}                                               [         NA         ]
                    |
                    `->{2}                                               [         NA         ]

             ->{4}                                                       [         NA         ]

             ->{3}                                                       [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {3}: MAYBE
             ---------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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:
                 {  *top*_0^#(inf_1(x)) -> c_2(*top*_0^#(cons_0(x, inf_1(s_0(x)))))
                  , s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                  , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                  , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                  , cons_1(x, cons_1(y, z)) -> big_0()
                  , cons_1(x, cons_0(y, z)) -> big_0()}

             Proof Output:
               The input cannot be shown compatible

           * Path {4}: NA
             ------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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.

           * Path {5}: inherited
             -------------------

             This path is subsumed by the proof of path {5}->{6}->{1}.

           * Path {5}->{6}: inherited
             ------------------------

             This path is subsumed by the proof of path {5}->{6}->{1}.

           * Path {5}->{6}->{1}: NA
             ----------------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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.

           * Path {5}->{6}->{2}: NA
             ----------------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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: cons_1^#(x, cons_1(y, z)) -> c_0()
              , 2: cons_1^#(x, cons_0(y, z)) -> c_1()
              , 3: *top*_0^#(inf_1(x)) ->
                   c_2(*top*_0^#(cons_0(x, inf_1(s_0(x)))))
              , 4: s_0^#(inf_1(x)) -> c_3(s_0^#(cons_0(x, inf_1(s_0(x)))))
              , 5: cons_0^#(inf_1(x), x0) ->
                   c_4(cons_0^#(cons_0(x, inf_1(s_0(x))), x0))
              , 6: cons_0^#(x0, inf_1(x)) ->
                   c_5(cons_1^#(x0, cons_0(x, inf_1(s_0(x)))))}

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

             ->{5}                                                       [     inherited      ]
                |
                `->{6}                                                   [     inherited      ]
                    |
                    |->{1}                                               [         NA         ]
                    |
                    `->{2}                                               [         NA         ]

             ->{4}                                                       [       MAYBE        ]

             ->{3}                                                       [         NA         ]



         Sub-problems:
         -------------
           * Path {3}: NA
             ------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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.

           * Path {4}: MAYBE
             ---------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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:
                 {  s_0^#(inf_1(x)) -> c_3(s_0^#(cons_0(x, inf_1(s_0(x)))))
                  , s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                  , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                  , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                  , cons_1(x, cons_1(y, z)) -> big_0()
                  , cons_1(x, cons_0(y, z)) -> big_0()}

             Proof Output:
               The input cannot be shown compatible

           * Path {5}: inherited
             -------------------

             This path is subsumed by the proof of path {5}->{6}->{1}.

           * Path {5}->{6}: inherited
             ------------------------

             This path is subsumed by the proof of path {5}->{6}->{1}.

           * Path {5}->{6}->{1}: NA
             ----------------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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.

           * Path {5}->{6}->{2}: NA
             ----------------------

             The usable rules for this path are:

               {  s_0(inf_1(x)) -> s_0(cons_0(x, inf_1(s_0(x))))
                , cons_0(inf_1(x), x0) -> cons_0(cons_0(x, inf_1(s_0(x))), x0)
                , cons_0(x0, inf_1(x)) -> cons_1(x0, cons_0(x, inf_1(s_0(x))))
                , cons_1(x, cons_1(y, z)) -> big_0()
                , cons_1(x, cons_0(y, z)) -> big_0()}

             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.