Problem Transformed outermost 08 ex5.8

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed outermost 08 ex5.8

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	MAYBE
Input	Transformed outermost 08 ex5.8

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  from_2(x) -> cons_0(x, from_1(s_0(x)))
     , from_3(x) -> cons_0(x, from_2(s_0(x)))
     , from_4(x) -> cons_0(x, from_2(s_0(x)))
     , from_1(x) -> cons_1(x, from_1(s_0(x)))
     , cons_1(s_0(s_0(x)), xs) -> nil_0()}

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: from_2^#(x) -> c_0(from_1^#(s_0(x)))
              , 2: from_3^#(x) -> c_1(from_2^#(s_0(x)))
              , 3: from_4^#(x) -> c_2(from_2^#(s_0(x)))
              , 4: from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
              , 5: cons_1^#(s_0(s_0(x)), xs) -> c_4()}

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

             ->{3}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [         NA         ]

             ->{2}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [         NA         ]



         Sub-problems:
         -------------
           * Path {2}: inherited
             -------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

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

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}->{5}: NA
             ---------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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 {3}: inherited
             -------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}: inherited
             ------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}->{5}: NA
             ---------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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: from_2^#(x) -> c_0(from_1^#(s_0(x)))
              , 2: from_3^#(x) -> c_1(from_2^#(s_0(x)))
              , 3: from_4^#(x) -> c_2(from_2^#(s_0(x)))
              , 4: from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
              , 5: cons_1^#(s_0(s_0(x)), xs) -> c_4()}

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

             ->{3}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [         NA         ]

             ->{2}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {2}: inherited
             -------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

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

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}->{5}: MAYBE
             ------------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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:
                 {  from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
                  , from_2^#(x) -> c_0(from_1^#(s_0(x)))
                  , from_3^#(x) -> c_1(from_2^#(s_0(x)))
                  , cons_1^#(s_0(s_0(x)), xs) -> c_4()
                  , from_1(x) -> cons_1(x, from_1(s_0(x)))
                  , cons_1(s_0(s_0(x)), xs) -> nil_0()}

             Proof Output:
               The input cannot be shown compatible

           * Path {3}: inherited
             -------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}: inherited
             ------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}->{5}: NA
             ---------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:

             {  1: from_2^#(x) -> c_0(from_1^#(s_0(x)))
              , 2: from_3^#(x) -> c_1(from_2^#(s_0(x)))
              , 3: from_4^#(x) -> c_2(from_2^#(s_0(x)))
              , 4: from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
              , 5: cons_1^#(s_0(s_0(x)), xs) -> c_4()}

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

             ->{3}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [         NA         ]

             ->{2}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {2}: inherited
             -------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

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

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}->{5}: MAYBE
             ------------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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:
                 {  from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
                  , from_2^#(x) -> c_0(from_1^#(s_0(x)))
                  , from_3^#(x) -> c_1(from_2^#(s_0(x)))
                  , cons_1^#(s_0(s_0(x)), xs) -> c_4()
                  , from_1(x) -> cons_1(x, from_1(s_0(x)))
                  , cons_1(s_0(s_0(x)), xs) -> nil_0()}

             Proof Output:
               The input cannot be shown compatible

           * Path {3}: inherited
             -------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}: inherited
             ------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}->{5}: NA
             ---------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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.

    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	Transformed outermost 08 ex5.8

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	MAYBE
Input	Transformed outermost 08 ex5.8

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    runtime-complexity with respect to
  Rules:
    {  from_2(x) -> cons_0(x, from_1(s_0(x)))
     , from_3(x) -> cons_0(x, from_2(s_0(x)))
     , from_4(x) -> cons_0(x, from_2(s_0(x)))
     , from_1(x) -> cons_1(x, from_1(s_0(x)))
     , cons_1(s_0(s_0(x)), xs) -> nil_0()}

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: from_2^#(x) -> c_0(x, from_1^#(s_0(x)))
              , 2: from_3^#(x) -> c_1(x, from_2^#(s_0(x)))
              , 3: from_4^#(x) -> c_2(x, from_2^#(s_0(x)))
              , 4: from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
              , 5: cons_1^#(s_0(s_0(x)), xs) -> c_4()}

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

             ->{3}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [         NA         ]

             ->{2}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [         NA         ]



         Sub-problems:
         -------------
           * Path {2}: inherited
             -------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

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

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}->{5}: NA
             ---------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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 {3}: inherited
             -------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}: inherited
             ------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}->{5}: NA
             ---------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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: from_2^#(x) -> c_0(x, from_1^#(s_0(x)))
              , 2: from_3^#(x) -> c_1(x, from_2^#(s_0(x)))
              , 3: from_4^#(x) -> c_2(x, from_2^#(s_0(x)))
              , 4: from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
              , 5: cons_1^#(s_0(s_0(x)), xs) -> c_4()}

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

             ->{3}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [         NA         ]

             ->{2}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {2}: inherited
             -------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

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

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}->{5}: MAYBE
             ------------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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:
                 {  from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
                  , from_2^#(x) -> c_0(x, from_1^#(s_0(x)))
                  , from_3^#(x) -> c_1(x, from_2^#(s_0(x)))
                  , cons_1^#(s_0(s_0(x)), xs) -> c_4()
                  , from_1(x) -> cons_1(x, from_1(s_0(x)))
                  , cons_1(s_0(s_0(x)), xs) -> nil_0()}

             Proof Output:
               The input cannot be shown compatible

           * Path {3}: inherited
             -------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}: inherited
             ------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}->{5}: NA
             ---------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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) 'wdg' failed due to the following reason:
         Transformation Details:
         -----------------------
           We have computed the following set of weak (innermost) dependency pairs:

             {  1: from_2^#(x) -> c_0(x, from_1^#(s_0(x)))
              , 2: from_3^#(x) -> c_1(x, from_2^#(s_0(x)))
              , 3: from_4^#(x) -> c_2(x, from_2^#(s_0(x)))
              , 4: from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
              , 5: cons_1^#(s_0(s_0(x)), xs) -> c_4()}

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

             ->{3}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [         NA         ]

             ->{2}                                                       [     inherited      ]
                |
                `->{1}                                                   [     inherited      ]
                    |
                    `->{4}                                               [     inherited      ]
                        |
                        `->{5}                                           [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {2}: inherited
             -------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

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

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {2}->{1}->{4}->{5}.

           * Path {2}->{1}->{4}->{5}: MAYBE
             ------------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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:
                 {  from_1^#(x) -> c_3(cons_1^#(x, from_1(s_0(x))))
                  , from_2^#(x) -> c_0(x, from_1^#(s_0(x)))
                  , from_3^#(x) -> c_1(x, from_2^#(s_0(x)))
                  , cons_1^#(s_0(s_0(x)), xs) -> c_4()
                  , from_1(x) -> cons_1(x, from_1(s_0(x)))
                  , cons_1(s_0(s_0(x)), xs) -> nil_0()}

             Proof Output:
               The input cannot be shown compatible

           * Path {3}: inherited
             -------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}: inherited
             ------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}: inherited
             -----------------------------

             This path is subsumed by the proof of path {3}->{1}->{4}->{5}.

           * Path {3}->{1}->{4}->{5}: NA
             ---------------------------

             The usable rules for this path are:

               {  from_1(x) -> cons_1(x, from_1(s_0(x)))
                , cons_1(s_0(s_0(x)), xs) -> nil_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.

    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.