MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { h(X, Z) -> f(X, s(X), Z)
  , f(X, Y, g(X, Y)) -> h(0(), g(X, Y))
  , g(X, s(Y)) -> g(X, Y)
  , g(0(), Y) -> 0() }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      The weightgap principle applies (using the following nonconstant
      growth matrix-interpretation)
      
      The following argument positions are usable:
        none
      
      TcT has computed the following matrix interpretation satisfying
      not(EDA) and not(IDA(1)).
      
            [h](x1, x2) = [4]         
                                      
        [f](x1, x2, x3) = [0]         
                                      
                [s](x1) = [1] x1 + [7]
                                      
            [g](x1, x2) = [0]         
                                      
                    [0] = [5]         
      
      The following symbols are considered usable
      
        {h, f, g}
      
      The order satisfies the following ordering constraints:
      
                 [h(X, Z)] =  [4]              
                           >  [0]              
                           =  [f(X, s(X), Z)]  
                                               
        [f(X, Y, g(X, Y))] =  [0]              
                           ?  [4]              
                           =  [h(0(), g(X, Y))]
                                               
              [g(X, s(Y))] =  [0]              
                           >= [0]              
                           =  [g(X, Y)]        
                                               
               [g(0(), Y)] =  [0]              
                           ?  [5]              
                           =  [0()]            
                                               
      
      Further, it can be verified that all rules not oriented are covered by the weightgap condition.
      
      We are left with following problem, upon which TcT provides the
      certificate MAYBE.
      
      Strict Trs:
        { f(X, Y, g(X, Y)) -> h(0(), g(X, Y))
        , g(X, s(Y)) -> g(X, Y)
        , g(0(), Y) -> 0() }
      Weak Trs: { h(X, Z) -> f(X, s(X), Z) }
      Obligation:
        runtime complexity
      Answer:
        MAYBE
      
      The weightgap principle applies (using the following nonconstant
      growth matrix-interpretation)
      
      The following argument positions are usable:
        none
      
      TcT has computed the following matrix interpretation satisfying
      not(EDA) and not(IDA(1)).
      
            [h](x1, x2) = [1] x2 + [4]
                                      
        [f](x1, x2, x3) = [0]         
                                      
                [s](x1) = [1] x1 + [7]
                                      
            [g](x1, x2) = [4]         
                                      
                    [0] = [1]         
      
      The following symbols are considered usable
      
        {h, f, g}
      
      The order satisfies the following ordering constraints:
      
                 [h(X, Z)] =  [1] Z + [4]      
                           >  [0]              
                           =  [f(X, s(X), Z)]  
                                               
        [f(X, Y, g(X, Y))] =  [0]              
                           ?  [8]              
                           =  [h(0(), g(X, Y))]
                                               
              [g(X, s(Y))] =  [4]              
                           >= [4]              
                           =  [g(X, Y)]        
                                               
               [g(0(), Y)] =  [4]              
                           >  [1]              
                           =  [0()]            
                                               
      
      Further, it can be verified that all rules not oriented are covered by the weightgap condition.
      
      We are left with following problem, upon which TcT provides the
      certificate MAYBE.
      
      Strict Trs:
        { f(X, Y, g(X, Y)) -> h(0(), g(X, Y))
        , g(X, s(Y)) -> g(X, Y) }
      Weak Trs:
        { h(X, Z) -> f(X, s(X), Z)
        , g(0(), Y) -> 0() }
      Obligation:
        runtime complexity
      Answer:
        MAYBE
      
      The weightgap principle applies (using the following nonconstant
      growth matrix-interpretation)
      
      The following argument positions are usable:
        none
      
      TcT has computed the following matrix interpretation satisfying
      not(EDA) and not(IDA(1)).
      
            [h](x1, x2) = [1] x1 + [4]         
                                               
        [f](x1, x2, x3) = [1] x1 + [0]         
                                               
                [s](x1) = [1] x1 + [4]         
                                               
            [g](x1, x2) = [1] x1 + [1] x2 + [3]
                                               
                    [0] = [5]                  
      
      The following symbols are considered usable
      
        {h, f, g}
      
      The order satisfies the following ordering constraints:
      
                 [h(X, Z)] = [1] X + [4]        
                           > [1] X + [0]        
                           = [f(X, s(X), Z)]    
                                                
        [f(X, Y, g(X, Y))] = [1] X + [0]        
                           ? [9]                
                           = [h(0(), g(X, Y))]  
                                                
              [g(X, s(Y))] = [1] X + [1] Y + [7]
                           > [1] X + [1] Y + [3]
                           = [g(X, Y)]          
                                                
               [g(0(), Y)] = [1] Y + [8]        
                           > [5]                
                           = [0()]              
                                                
      
      Further, it can be verified that all rules not oriented are covered by the weightgap condition.
      
      We are left with following problem, upon which TcT provides the
      certificate MAYBE.
      
      Strict Trs: { f(X, Y, g(X, Y)) -> h(0(), g(X, Y)) }
      Weak Trs:
        { h(X, Z) -> f(X, s(X), Z)
        , g(X, s(Y)) -> g(X, Y)
        , g(0(), Y) -> 0() }
      Obligation:
        runtime complexity
      Answer:
        MAYBE
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'empty' failed due to the following reason:
         
         Empty strict component of the problem is NOT empty.
      
      2) 'WithProblem' failed due to the following reason:
         
         None of the processors succeeded.
         
         Details of failed attempt(s):
         -----------------------------
         1) 'empty' failed due to the following reason:
            
            Empty strict component of the problem is NOT empty.
         
         2) 'Fastest' failed due to the following reason:
            
            None of the processors succeeded.
            
            Details of failed attempt(s):
            -----------------------------
            1) 'WithProblem' failed due to the following reason:
               
               None of the processors succeeded.
               
               Details of failed attempt(s):
               -----------------------------
               1) 'empty' failed due to the following reason:
                  
                  Empty strict component of the problem is NOT empty.
               
               2) 'WithProblem' failed due to the following reason:
                  
                  Empty strict component of the problem is NOT empty.
               
            
            2) 'WithProblem' failed due to the following reason:
               
               None of the processors succeeded.
               
               Details of failed attempt(s):
               -----------------------------
               1) 'empty' failed due to the following reason:
                  
                  Empty strict component of the problem is NOT empty.
               
               2) 'WithProblem' failed due to the following reason:
                  
                  None of the processors succeeded.
                  
                  Details of failed attempt(s):
                  -----------------------------
                  1) 'empty' failed due to the following reason:
                     
                     Empty strict component of the problem is NOT empty.
                  
                  2) 'WithProblem' failed due to the following reason:
                     
                     None of the processors succeeded.
                     
                     Details of failed attempt(s):
                     -----------------------------
                     1) 'empty' failed due to the following reason:
                        
                        Empty strict component of the problem is NOT empty.
                     
                     2) 'WithProblem' failed due to the following reason:
                        
                        Empty strict component of the problem is NOT empty.
                     
                  
               
            
         
      
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { h^#(X, Z) -> c_1(f^#(X, s(X), Z))
     , f^#(X, Y, g(X, Y)) -> c_2(h^#(0(), g(X, Y)))
     , g^#(X, s(Y)) -> c_3(g^#(X, Y))
     , g^#(0(), Y) -> c_4() }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { h^#(X, Z) -> c_1(f^#(X, s(X), Z))
     , f^#(X, Y, g(X, Y)) -> c_2(h^#(0(), g(X, Y)))
     , g^#(X, s(Y)) -> c_3(g^#(X, Y))
     , g^#(0(), Y) -> c_4() }
   Strict Trs:
     { h(X, Z) -> f(X, s(X), Z)
     , f(X, Y, g(X, Y)) -> h(0(), g(X, Y))
     , g(X, s(Y)) -> g(X, Y)
     , g(0(), Y) -> 0() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {4} by applications of
   Pre({4}) = {3}. Here rules are labeled as follows:
   
     DPs:
       { 1: h^#(X, Z) -> c_1(f^#(X, s(X), Z))
       , 2: f^#(X, Y, g(X, Y)) -> c_2(h^#(0(), g(X, Y)))
       , 3: g^#(X, s(Y)) -> c_3(g^#(X, Y))
       , 4: g^#(0(), Y) -> c_4() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { h^#(X, Z) -> c_1(f^#(X, s(X), Z))
     , f^#(X, Y, g(X, Y)) -> c_2(h^#(0(), g(X, Y)))
     , g^#(X, s(Y)) -> c_3(g^#(X, Y)) }
   Strict Trs:
     { h(X, Z) -> f(X, s(X), Z)
     , f(X, Y, g(X, Y)) -> h(0(), g(X, Y))
     , g(X, s(Y)) -> g(X, Y)
     , g(0(), Y) -> 0() }
   Weak DPs: { g^#(0(), Y) -> c_4() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..