MAYBE

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

Strict Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , and(tt(), X) -> activate(X)
  , activate(X) -> X
  , activate(n__zeros()) -> zeros()
  , length(cons(N, L)) -> s(length(activate(L)))
  , length(nil()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { zeros^#() -> c_1()
  , zeros^#() -> c_2()
  , and^#(tt(), X) -> c_3(activate^#(X))
  , activate^#(X) -> c_4()
  , activate^#(n__zeros()) -> c_5(zeros^#())
  , length^#(cons(N, L)) -> c_6(length^#(activate(L)))
  , length^#(nil()) -> c_7() }

and mark the set of starting terms.

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

Strict DPs:
  { zeros^#() -> c_1()
  , zeros^#() -> c_2()
  , and^#(tt(), X) -> c_3(activate^#(X))
  , activate^#(X) -> c_4()
  , activate^#(n__zeros()) -> c_5(zeros^#())
  , length^#(cons(N, L)) -> c_6(length^#(activate(L)))
  , length^#(nil()) -> c_7() }
Strict Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , and(tt(), X) -> activate(X)
  , activate(X) -> X
  , activate(n__zeros()) -> zeros()
  , length(cons(N, L)) -> s(length(activate(L)))
  , length(nil()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Strict Usable Rules:
    { zeros() -> cons(0(), n__zeros())
    , zeros() -> n__zeros()
    , activate(X) -> X
    , activate(n__zeros()) -> zeros() }

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

Strict DPs:
  { zeros^#() -> c_1()
  , zeros^#() -> c_2()
  , and^#(tt(), X) -> c_3(activate^#(X))
  , activate^#(X) -> c_4()
  , activate^#(n__zeros()) -> c_5(zeros^#())
  , length^#(cons(N, L)) -> c_6(length^#(activate(L)))
  , length^#(nil()) -> c_7() }
Strict Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , activate(X) -> X
  , activate(n__zeros()) -> zeros() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(c_3) = {1}, Uargs(c_5) = {1}, Uargs(length^#) = {1},
  Uargs(c_6) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

           [zeros] = [2]                  
                                          
    [cons](x1, x2) = [1] x1 + [1] x2 + [0]
                                          
               [0] = [0]                  
                                          
        [n__zeros] = [1]                  
                                          
              [tt] = [1]                  
                                          
    [activate](x1) = [1] x1 + [2]         
                                          
             [nil] = [1]                  
                                          
         [zeros^#] = [1]                  
                                          
             [c_1] = [1]                  
                                          
             [c_2] = [1]                  
                                          
   [and^#](x1, x2) = [1] x1 + [2] x2 + [2]
                                          
         [c_3](x1) = [1] x1 + [1]         
                                          
  [activate^#](x1) = [2] x1 + [1]         
                                          
             [c_4] = [1]                  
                                          
         [c_5](x1) = [1] x1 + [2]         
                                          
    [length^#](x1) = [2] x1 + [2]         
                                          
         [c_6](x1) = [1] x1 + [1]         
                                          
             [c_7] = [1]                  

This order satisfies following ordering constraints:

               [zeros()] = [2]                    
                         > [1]                    
                         = [cons(0(), n__zeros())]
                                                  
               [zeros()] = [2]                    
                         > [1]                    
                         = [n__zeros()]           
                                                  
           [activate(X)] = [1] X + [2]            
                         > [1] X + [0]            
                         = [X]                    
                                                  
  [activate(n__zeros())] = [3]                    
                         > [2]                    
                         = [zeros()]              
                                                  

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 DPs:
  { zeros^#() -> c_1()
  , zeros^#() -> c_2()
  , activate^#(X) -> c_4()
  , activate^#(n__zeros()) -> c_5(zeros^#())
  , length^#(cons(N, L)) -> c_6(length^#(activate(L))) }
Weak DPs:
  { and^#(tt(), X) -> c_3(activate^#(X))
  , length^#(nil()) -> c_7() }
Weak Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , activate(X) -> X
  , activate(n__zeros()) -> zeros() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,2} by applications of
Pre({1,2}) = {4}. Here rules are labeled as follows:

  DPs:
    { 1: zeros^#() -> c_1()
    , 2: zeros^#() -> c_2()
    , 3: activate^#(X) -> c_4()
    , 4: activate^#(n__zeros()) -> c_5(zeros^#())
    , 5: length^#(cons(N, L)) -> c_6(length^#(activate(L)))
    , 6: and^#(tt(), X) -> c_3(activate^#(X))
    , 7: length^#(nil()) -> c_7() }

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

Strict DPs:
  { activate^#(X) -> c_4()
  , activate^#(n__zeros()) -> c_5(zeros^#())
  , length^#(cons(N, L)) -> c_6(length^#(activate(L))) }
Weak DPs:
  { zeros^#() -> c_1()
  , zeros^#() -> c_2()
  , and^#(tt(), X) -> c_3(activate^#(X))
  , length^#(nil()) -> c_7() }
Weak Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , activate(X) -> X
  , activate(n__zeros()) -> zeros() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ zeros^#() -> c_1()
, zeros^#() -> c_2()
, length^#(nil()) -> c_7() }

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

Strict DPs:
  { activate^#(X) -> c_4()
  , activate^#(n__zeros()) -> c_5(zeros^#())
  , length^#(cons(N, L)) -> c_6(length^#(activate(L))) }
Weak DPs: { and^#(tt(), X) -> c_3(activate^#(X)) }
Weak Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , activate(X) -> X
  , activate(n__zeros()) -> zeros() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

  { activate^#(n__zeros()) -> c_5(zeros^#()) }

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

Strict DPs:
  { activate^#(X) -> c_1()
  , activate^#(n__zeros()) -> c_2()
  , length^#(cons(N, L)) -> c_3(length^#(activate(L))) }
Weak DPs: { and^#(tt(), X) -> c_4(activate^#(X)) }
Weak Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , activate(X) -> X
  , activate(n__zeros()) -> zeros() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Consider the dependency graph

  1: activate^#(X) -> c_1()
  
  2: activate^#(n__zeros()) -> c_2()
  
  3: length^#(cons(N, L)) -> c_3(length^#(activate(L)))
     -->_1 length^#(cons(N, L)) -> c_3(length^#(activate(L))) :3
  
  4: and^#(tt(), X) -> c_4(activate^#(X))
     -->_1 activate^#(n__zeros()) -> c_2() :2
     -->_1 activate^#(X) -> c_1() :1
  

Following roots of the dependency graph are removed, as the
considered set of starting terms is closed under reduction with
respect to these rules (modulo compound contexts).

  { and^#(tt(), X) -> c_4(activate^#(X)) }


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

Strict DPs:
  { activate^#(X) -> c_1()
  , activate^#(n__zeros()) -> c_2()
  , length^#(cons(N, L)) -> c_3(length^#(activate(L))) }
Weak Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , activate(X) -> X
  , activate(n__zeros()) -> zeros() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Consider the dependency graph

  1: activate^#(X) -> c_1()
  
  2: activate^#(n__zeros()) -> c_2()
  
  3: length^#(cons(N, L)) -> c_3(length^#(activate(L)))
     -->_1 length^#(cons(N, L)) -> c_3(length^#(activate(L))) :3
  

Following roots of the dependency graph are removed, as the
considered set of starting terms is closed under reduction with
respect to these rules (modulo compound contexts).

  { activate^#(X) -> c_1()
  , activate^#(n__zeros()) -> c_2() }


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

Strict DPs: { length^#(cons(N, L)) -> c_3(length^#(activate(L))) }
Weak Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , activate(X) -> X
  , activate(n__zeros()) -> zeros() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'matrices' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'matrix interpretation of dimension 4' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   2) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   3) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   4) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   5) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   6) 'matrix interpretation of dimension 1' failed due to the
      following reason:
      
      The input cannot be shown compatible
   

2) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.


Arrrr..