MAYBE

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

Strict Trs:
  { zeros() -> cons(0(), zeros())
  , U11(tt(), L) -> U12(tt(), L)
  , U12(tt(), L) -> s(length(L))
  , length(cons(N, L)) -> U11(tt(), L)
  , length(nil()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { zeros^#() -> c_1(zeros^#())
  , U11^#(tt(), L) -> c_2(U12^#(tt(), L))
  , U12^#(tt(), L) -> c_3(length^#(L))
  , length^#(cons(N, L)) -> c_4(U11^#(tt(), L))
  , length^#(nil()) -> c_5() }

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^#())
  , U11^#(tt(), L) -> c_2(U12^#(tt(), L))
  , U12^#(tt(), L) -> c_3(length^#(L))
  , length^#(cons(N, L)) -> c_4(U11^#(tt(), L))
  , length^#(nil()) -> c_5() }
Strict Trs:
  { zeros() -> cons(0(), zeros())
  , U11(tt(), L) -> U12(tt(), L)
  , U12(tt(), L) -> s(length(L))
  , length(cons(N, L)) -> U11(tt(), L)
  , length(nil()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

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

Strict DPs:
  { zeros^#() -> c_1(zeros^#())
  , U11^#(tt(), L) -> c_2(U12^#(tt(), L))
  , U12^#(tt(), L) -> c_3(length^#(L))
  , length^#(cons(N, L)) -> c_4(U11^#(tt(), L))
  , length^#(nil()) -> c_5() }
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_1) = {1}, Uargs(c_2) = {1}, Uargs(c_3) = {1},
  Uargs(c_4) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

   [cons](x1, x2) = [1] x2 + [1]
                                
             [tt] = [0]         
                                
            [nil] = [2]         
                                
        [zeros^#] = [2]         
                                
        [c_1](x1) = [1] x1 + [1]
                                
  [U11^#](x1, x2) = [0]         
                                
        [c_2](x1) = [1] x1 + [1]
                                
  [U12^#](x1, x2) = [0]         
                                
        [c_3](x1) = [1] x1 + [1]
                                
   [length^#](x1) = [1]         
                                
        [c_4](x1) = [1] x1 + [1]
                                
            [c_5] = [0]         

This order satisfies following ordering constraints:


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^#())
  , U11^#(tt(), L) -> c_2(U12^#(tt(), L))
  , U12^#(tt(), L) -> c_3(length^#(L))
  , length^#(cons(N, L)) -> c_4(U11^#(tt(), L)) }
Weak DPs: { length^#(nil()) -> c_5() }
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.

{ length^#(nil()) -> c_5() }

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

Strict DPs:
  { zeros^#() -> c_1(zeros^#())
  , U11^#(tt(), L) -> c_2(U12^#(tt(), L))
  , U12^#(tt(), L) -> c_3(length^#(L))
  , length^#(cons(N, L)) -> c_4(U11^#(tt(), L)) }
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..