Problem Mixed outermost non-lin3

Tool CaT

Execution TimeUnknown
Answer
MAYBE
InputMixed outermost non-lin3

stdout:

MAYBE

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

Proof:
 Open

Tool IRC1

Execution TimeUnknown
Answer
MAYBE
InputMixed outermost non-lin3

stdout:

MAYBE
 Warning when parsing problem:
                             
                               Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution TimeUnknown
Answer
MAYBE
InputMixed outermost non-lin3

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  g(x, x) -> f(f(x, x), x)
     , f(x, x) -> g(g(x, x), x)
     , f(x, y) -> 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^#(x, x) -> c_0(f^#(f(x, x), x))
              , 2: f^#(x, x) -> c_1(g^#(g(x, x), x))
              , 3: f^#(x, y) -> c_2()}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{1,2}                                                     [     inherited      ]
                |
                `->{3}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * 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:
             
               {  g(x, x) -> f(f(x, x), x)
                , f(x, x) -> g(g(x, x), x)
                , f(x, y) -> 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 3'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    innermost runtime-complexity with respect to
               Rules:
                 {  g^#(x, x) -> c_0(f^#(f(x, x), x))
                  , f^#(x, x) -> c_1(g^#(g(x, x), x))
                  , f^#(x, y) -> c_2()
                  , g(x, x) -> f(f(x, x), x)
                  , f(x, x) -> g(g(x, x), x)
                  , f(x, y) -> y}
             
             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: g^#(x, x) -> c_0(f^#(f(x, x), x))
              , 2: f^#(x, x) -> c_1(g^#(g(x, x), x))
              , 3: f^#(x, y) -> c_2()}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{1,2}                                                     [     inherited      ]
                |
                `->{3}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * 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:
             
               {  g(x, x) -> f(f(x, x), x)
                , f(x, x) -> g(g(x, x), x)
                , f(x, y) -> 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^#(x, x) -> c_0(f^#(f(x, x), x))
                  , f^#(x, x) -> c_1(g^#(g(x, x), x))
                  , f^#(x, y) -> c_2()
                  , g(x, x) -> f(f(x, x), x)
                  , f(x, x) -> g(g(x, x), x)
                  , f(x, y) -> 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^#(x, x) -> c_0(f^#(f(x, x), x))
              , 2: f^#(x, x) -> c_1(g^#(g(x, x), x))
              , 3: f^#(x, y) -> c_2()}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{1,2}                                                     [     inherited      ]
                |
                `->{3}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * 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:
             
               {  g(x, x) -> f(f(x, x), x)
                , f(x, x) -> g(g(x, x), x)
                , f(x, y) -> 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^#(x, x) -> c_0(f^#(f(x, x), x))
                  , f^#(x, x) -> c_1(g^#(g(x, x), x))
                  , f^#(x, y) -> c_2()
                  , g(x, x) -> f(f(x, x), x)
                  , f(x, x) -> g(g(x, x), x)
                  , f(x, y) -> 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 TimeUnknown
Answer
MAYBE
InputMixed outermost non-lin3

stdout:

MAYBE
 Warning when parsing problem:
                             
                               Unsupported strategy 'OUTERMOST'

Tool RC2

Execution TimeUnknown
Answer
MAYBE
InputMixed outermost non-lin3

stdout:

MAYBE

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           MAYBE
Input Problem:    runtime-complexity with respect to
  Rules:
    {  g(x, x) -> f(f(x, x), x)
     , f(x, x) -> g(g(x, x), x)
     , f(x, y) -> 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^#(x, x) -> c_0(f^#(f(x, x), x))
              , 2: f^#(x, x) -> c_1(g^#(g(x, x), x))
              , 3: f^#(x, y) -> c_2(y)}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{1,2}                                                     [     inherited      ]
                |
                `->{3}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * 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:
             
               {  g(x, x) -> f(f(x, x), x)
                , f(x, x) -> g(g(x, x), x)
                , f(x, y) -> 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 3'
             --------------------------------------
             Answer:           MAYBE
             Input Problem:    runtime-complexity with respect to
               Rules:
                 {  g^#(x, x) -> c_0(f^#(f(x, x), x))
                  , f^#(x, x) -> c_1(g^#(g(x, x), x))
                  , f^#(x, y) -> c_2(y)
                  , g(x, x) -> f(f(x, x), x)
                  , f(x, x) -> g(g(x, x), x)
                  , f(x, y) -> y}
             
             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: g^#(x, x) -> c_0(f^#(f(x, x), x))
              , 2: f^#(x, x) -> c_1(g^#(g(x, x), x))
              , 3: f^#(x, y) -> c_2(y)}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{1,2}                                                     [     inherited      ]
                |
                `->{3}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * 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:
             
               {  g(x, x) -> f(f(x, x), x)
                , f(x, x) -> g(g(x, x), x)
                , f(x, y) -> 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^#(x, x) -> c_0(f^#(f(x, x), x))
                  , f^#(x, x) -> c_1(g^#(g(x, x), x))
                  , f^#(x, y) -> c_2(y)
                  , g(x, x) -> f(f(x, x), x)
                  , f(x, x) -> g(g(x, x), x)
                  , f(x, y) -> 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^#(x, x) -> c_0(f^#(f(x, x), x))
              , 2: f^#(x, x) -> c_1(g^#(g(x, x), x))
              , 3: f^#(x, y) -> c_2(y)}
           
           Following Dependency Graph (modulo SCCs) was computed. (Answers to
           subproofs are indicated to the right.)
           
             ->{1,2}                                                     [     inherited      ]
                |
                `->{3}                                                   [       MAYBE        ]
             
           
         
         Sub-problems:
         -------------
           * 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:
             
               {  g(x, x) -> f(f(x, x), x)
                , f(x, x) -> g(g(x, x), x)
                , f(x, y) -> 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^#(x, x) -> c_0(f^#(f(x, x), x))
                  , f^#(x, x) -> c_1(g^#(g(x, x), x))
                  , f^#(x, y) -> c_2(y)
                  , g(x, x) -> f(f(x, x), x)
                  , f(x, x) -> g(g(x, x), x)
                  , f(x, y) -> 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.