Problem HirokawaMiddeldorp 04 n007

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	HirokawaMiddeldorp 04 n007

stdout:

MAYBE

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

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	HirokawaMiddeldorp 04 n007

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	MAYBE
Input	HirokawaMiddeldorp 04 n007

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(x, y) -> f(x, x)
     , f(s(x), y) -> f(y, 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: f^#(x, y) -> c_0(f^#(x, x))
              , 2: f^#(s(x), y) -> c_1(f^#(y, x))}

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

             ->{1,2}                                                     [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1,2}: MAYBE
             -----------------

             The usable rules of this path are empty.

             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(f) = {}, Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
                 Uargs(c_1) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                f(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                            [0 0 0]      [0 0 0]      [0]
                            [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 3 3] x1 + [0]
                        [0 1 3]      [0]
                        [0 0 1]      [0]
                f^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [3 3 3]      [3 3 3]      [0]
                              [3 3 3]      [3 3 3]      [0]
                c_0(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]

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

             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules:
                 {  f^#(x, y) -> c_0(f^#(x, x))
                  , f^#(s(x), y) -> c_1(f^#(y, x))}
               Weak Rules: {}

             Proof Output:
               The input cannot be shown compatible

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

             {  1: f^#(x, y) -> c_0(f^#(x, x))
              , 2: f^#(s(x), y) -> c_1(f^#(y, x))}

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

             ->{1,2}                                                     [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1,2}: MAYBE
             -----------------

             The usable rules of this path are empty.

             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(f) = {}, Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
                 Uargs(c_1) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                f(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                            [0 0]      [0 0]      [0]
                s(x1) = [1 3] x1 + [0]
                        [0 1]      [0]
                f^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [3 3]      [3 3]      [0]
                c_0(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]

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

             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules:
                 {  f^#(x, y) -> c_0(f^#(x, x))
                  , f^#(s(x), y) -> c_1(f^#(y, x))}
               Weak Rules: {}

             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: f^#(x, y) -> c_0(f^#(x, x))
              , 2: f^#(s(x), y) -> c_1(f^#(y, x))}

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

             ->{1,2}                                                     [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1,2}: MAYBE
             -----------------

             The usable rules of this path are empty.

             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(f) = {}, Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
                 Uargs(c_1) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                f(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [0]
                f^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [1] x1 + [0]
                c_1(x1) = [1] x1 + [0]

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

             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost DP runtime-complexity with respect to
               Strict Rules:
                 {  f^#(x, y) -> c_0(f^#(x, x))
                  , f^#(s(x), y) -> c_1(f^#(y, x))}
               Weak Rules: {}

             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	HirokawaMiddeldorp 04 n007

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	MAYBE
Input	HirokawaMiddeldorp 04 n007

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    runtime-complexity with respect to
  Rules:
    {  f(x, y) -> f(x, x)
     , f(s(x), y) -> f(y, 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: f^#(x, y) -> c_0(f^#(x, x))
              , 2: f^#(s(x), y) -> c_1(f^#(y, x))}

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

             ->{1,2}                                                     [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1,2}: MAYBE
             -----------------

             The usable rules of this path are empty.

             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(f) = {}, Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
                 Uargs(c_1) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                f(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                            [0 0 0]      [0 0 0]      [0]
                            [0 0 0]      [0 0 0]      [0]
                s(x1) = [1 3 3] x1 + [0]
                        [0 1 3]      [0]
                        [0 0 1]      [0]
                f^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
                              [3 3 3]      [3 3 3]      [0]
                              [3 3 3]      [3 3 3]      [0]
                c_0(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]
                c_1(x1) = [1 0 0] x1 + [0]
                          [0 1 0]      [0]
                          [0 0 1]      [0]

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

             'matrix-interpretation of dimension 3'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules:
                 {  f^#(x, y) -> c_0(f^#(x, x))
                  , f^#(s(x), y) -> c_1(f^#(y, x))}
               Weak Rules: {}

             Proof Output:
               The input cannot be shown compatible

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

             {  1: f^#(x, y) -> c_0(f^#(x, x))
              , 2: f^#(s(x), y) -> c_1(f^#(y, x))}

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

             ->{1,2}                                                     [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1,2}: MAYBE
             -----------------

             The usable rules of this path are empty.

             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(f) = {}, Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
                 Uargs(c_1) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                f(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                            [0 0]      [0 0]      [0]
                s(x1) = [1 3] x1 + [0]
                        [0 1]      [0]
                f^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
                              [3 3]      [3 3]      [0]
                c_0(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
                c_1(x1) = [1 0] x1 + [0]
                          [0 1]      [0]

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

             'matrix-interpretation of dimension 2'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules:
                 {  f^#(x, y) -> c_0(f^#(x, x))
                  , f^#(s(x), y) -> c_1(f^#(y, x))}
               Weak Rules: {}

             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: f^#(x, y) -> c_0(f^#(x, x))
              , 2: f^#(s(x), y) -> c_1(f^#(y, x))}

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

             ->{1,2}                                                     [       MAYBE        ]



         Sub-problems:
         -------------
           * Path {1,2}: MAYBE
             -----------------

             The usable rules of this path are empty.

             The weightgap principle applies, using the following adequate RMI:
               The following argument positions are usable:
                 Uargs(f) = {}, Uargs(s) = {}, Uargs(f^#) = {}, Uargs(c_0) = {1},
                 Uargs(c_1) = {1}
               We have the following constructor-restricted matrix interpretation:
               Interpretation Functions:
                f(x1, x2) = [0] x1 + [0] x2 + [0]
                s(x1) = [1] x1 + [0]
                f^#(x1, x2) = [0] x1 + [0] x2 + [0]
                c_0(x1) = [1] x1 + [0]
                c_1(x1) = [1] x1 + [0]

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

             'matrix-interpretation of dimension 1'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    DP runtime-complexity with respect to
               Strict Rules:
                 {  f^#(x, y) -> c_0(f^#(x, x))
                  , f^#(s(x), y) -> c_1(f^#(y, x))}
               Weak Rules: {}

             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.