MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            from(X) -> cons(X,from(s(X)))
            length(cons(X,Y)) -> s(length1(Y))
            length(nil()) -> 0()
            length1(X) -> length(X)
        - Signature:
            {from/1,length/1,length1/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {from,length,length1} and constructors {0,cons,nil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        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))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - 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))
        - Weak TRS:
            from(X) -> cons(X,from(s(X)))
            length(cons(X,Y)) -> s(length1(Y))
            length(nil()) -> 0()
            length1(X) -> length(X)
        - Signature:
            {from/1,length/1,length1/1,from#/1,length#/1,length1#/1} / {0/0,cons/2,nil/0,s/1,c_1/1,c_2/1,c_3/0,c_4/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {from#,length#,length1#} and constructors {0,cons,nil,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          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))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - 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))
        - Signature:
            {from/1,length/1,length1/1,from#/1,length#/1,length1#/1} / {0/0,cons/2,nil/0,s/1,c_1/1,c_2/1,c_3/0,c_4/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {from#,length#,length1#} and constructors {0,cons,nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3}
        by application of
          Pre({3}) = {4}.
        Here rules are labelled as follows:
          1: from#(X) -> c_1(from#(s(X)))
          2: length#(cons(X,Y)) -> c_2(length1#(Y))
          3: length#(nil()) -> c_3()
          4: length1#(X) -> c_4(length#(X))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            from#(X) -> c_1(from#(s(X)))
            length#(cons(X,Y)) -> c_2(length1#(Y))
            length1#(X) -> c_4(length#(X))
        - Weak DPs:
            length#(nil()) -> c_3()
        - Signature:
            {from/1,length/1,length1/1,from#/1,length#/1,length1#/1} / {0/0,cons/2,nil/0,s/1,c_1/1,c_2/1,c_3/0,c_4/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {from#,length#,length1#} and constructors {0,cons,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:from#(X) -> c_1(from#(s(X)))
             -->_1 from#(X) -> c_1(from#(s(X))):1
          
          2:S:length#(cons(X,Y)) -> c_2(length1#(Y))
             -->_1 length1#(X) -> c_4(length#(X)):3
          
          3:S:length1#(X) -> c_4(length#(X))
             -->_1 length#(nil()) -> c_3():4
             -->_1 length#(cons(X,Y)) -> c_2(length1#(Y)):2
          
          4:W:length#(nil()) -> c_3()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: length#(nil()) -> c_3()
* Step 5: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            from#(X) -> c_1(from#(s(X)))
            length#(cons(X,Y)) -> c_2(length1#(Y))
            length1#(X) -> c_4(length#(X))
        - Signature:
            {from/1,length/1,length1/1,from#/1,length#/1,length1#/1} / {0/0,cons/2,nil/0,s/1,c_1/1,c_2/1,c_3/0,c_4/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {from#,length#,length1#} and constructors {0,cons,nil,s}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            uargs(c_1) = {1},
            uargs(c_2) = {1},
            uargs(c_4) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                   p(0) = [0]         
                p(cons) = [0]         
                p(from) = [0]         
              p(length) = [0]         
             p(length1) = [1] x1 + [0]
                 p(nil) = [0]         
                   p(s) = [1]         
               p(from#) = [8] x1 + [4]
             p(length#) = [1]         
            p(length1#) = [0]         
                 p(c_1) = [1] x1 + [0]
                 p(c_2) = [1] x1 + [0]
                 p(c_3) = [0]         
                 p(c_4) = [1] x1 + [0]
          
          Following rules are strictly oriented:
          length#(cons(X,Y)) = [1]             
                             > [0]             
                             = c_2(length1#(Y))
          
          
          Following rules are (at-least) weakly oriented:
             from#(X) =  [8] X + [4]     
                      >= [12]            
                      =  c_1(from#(s(X)))
          
          length1#(X) =  [0]             
                      >= [1]             
                      =  c_4(length#(X)) 
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 6: Failure MAYBE
  + Considered Problem:
      - 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))
      - Signature:
          {from/1,length/1,length1/1,from#/1,length#/1,length1#/1} / {0/0,cons/2,nil/0,s/1,c_1/1,c_2/1,c_3/0,c_4/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {from#,length#,length1#} and constructors {0,cons,nil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE