MAYBE

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

Strict Trs:
  { from(X) -> cons(X, from(s(X)))
  , length(cons(X, Y)) -> s(length1(Y))
  , length(nil()) -> 0()
  , length1(X) -> length(X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { from^#(X) -> c_1(from^#(s(X)))
  , length^#(cons(X, Y)) -> c_2(length1^#(Y))
  , length^#(nil()) -> c_3()
  , length1^#(X) -> c_4(length^#(X)) }

and mark the set of starting terms.

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

Strict DPs:
  { from^#(X) -> c_1(from^#(s(X)))
  , length^#(cons(X, Y)) -> c_2(length1^#(Y))
  , length^#(nil()) -> c_3()
  , length1^#(X) -> c_4(length^#(X)) }
Strict Trs:
  { from(X) -> cons(X, from(s(X)))
  , length(cons(X, Y)) -> s(length1(Y))
  , length(nil()) -> 0()
  , length1(X) -> length(X) }
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:
  { from^#(X) -> c_1(from^#(s(X)))
  , length^#(cons(X, Y)) -> c_2(length1^#(Y))
  , length^#(nil()) -> c_3()
  , length1^#(X) -> c_4(length^#(X)) }
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_4) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

   [cons](x1, x2) = [1] x2 + [1]
                                
          [s](x1) = [1] x1 + [1]
                                
            [nil] = [2]         
                                
     [from^#](x1) = [1] x1 + [2]
                                
        [c_1](x1) = [1] x1 + [2]
                                
   [length^#](x1) = [2] x1 + [2]
                                
        [c_2](x1) = [1] x1 + [1]
                                
  [length1^#](x1) = [2] x1 + [1]
                                
            [c_3] = [1]         
                                
        [c_4](x1) = [1] x1 + [2]

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:
  { from^#(X) -> c_1(from^#(s(X)))
  , length1^#(X) -> c_4(length^#(X)) }
Weak DPs:
  { length^#(cons(X, Y)) -> c_2(length1^#(Y))
  , length^#(nil()) -> c_3() }
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_3() }

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

Strict DPs:
  { from^#(X) -> c_1(from^#(s(X)))
  , length1^#(X) -> c_4(length^#(X)) }
Weak DPs: { length^#(cons(X, Y)) -> c_2(length1^#(Y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..