MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
        - Signature:
            {first/2,from/1,sel/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {first,from,sel} and constructors {0,cons,nil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          first#(0(),Z) -> c_1()
          first#(s(X),cons(Y,Z)) -> c_2(first#(X,Z))
          from#(X) -> c_3(from#(s(X)))
          sel#(0(),cons(X,Z)) -> c_4()
          sel#(s(X),cons(Y,Z)) -> c_5(sel#(X,Z))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            first#(0(),Z) -> c_1()
            first#(s(X),cons(Y,Z)) -> c_2(first#(X,Z))
            from#(X) -> c_3(from#(s(X)))
            sel#(0(),cons(X,Z)) -> c_4()
            sel#(s(X),cons(Y,Z)) -> c_5(sel#(X,Z))
        - Weak TRS:
            first(0(),Z) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
            from(X) -> cons(X,from(s(X)))
            sel(0(),cons(X,Z)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,Z)
        - Signature:
            {first/2,from/1,sel/2,first#/2,from#/1,sel#/2} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0,c_5/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {first#,from#,sel#} and constructors {0,cons,nil,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          first#(0(),Z) -> c_1()
          first#(s(X),cons(Y,Z)) -> c_2(first#(X,Z))
          from#(X) -> c_3(from#(s(X)))
          sel#(0(),cons(X,Z)) -> c_4()
          sel#(s(X),cons(Y,Z)) -> c_5(sel#(X,Z))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            first#(0(),Z) -> c_1()
            first#(s(X),cons(Y,Z)) -> c_2(first#(X,Z))
            from#(X) -> c_3(from#(s(X)))
            sel#(0(),cons(X,Z)) -> c_4()
            sel#(s(X),cons(Y,Z)) -> c_5(sel#(X,Z))
        - Signature:
            {first/2,from/1,sel/2,first#/2,from#/1,sel#/2} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0,c_5/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {first#,from#,sel#} and constructors {0,cons,nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4}
        by application of
          Pre({1,4}) = {2,5}.
        Here rules are labelled as follows:
          1: first#(0(),Z) -> c_1()
          2: first#(s(X),cons(Y,Z)) -> c_2(first#(X,Z))
          3: from#(X) -> c_3(from#(s(X)))
          4: sel#(0(),cons(X,Z)) -> c_4()
          5: sel#(s(X),cons(Y,Z)) -> c_5(sel#(X,Z))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            first#(s(X),cons(Y,Z)) -> c_2(first#(X,Z))
            from#(X) -> c_3(from#(s(X)))
            sel#(s(X),cons(Y,Z)) -> c_5(sel#(X,Z))
        - Weak DPs:
            first#(0(),Z) -> c_1()
            sel#(0(),cons(X,Z)) -> c_4()
        - Signature:
            {first/2,from/1,sel/2,first#/2,from#/1,sel#/2} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0,c_5/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {first#,from#,sel#} and constructors {0,cons,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:first#(s(X),cons(Y,Z)) -> c_2(first#(X,Z))
             -->_1 first#(0(),Z) -> c_1():4
             -->_1 first#(s(X),cons(Y,Z)) -> c_2(first#(X,Z)):1
          
          2:S:from#(X) -> c_3(from#(s(X)))
             -->_1 from#(X) -> c_3(from#(s(X))):2
          
          3:S:sel#(s(X),cons(Y,Z)) -> c_5(sel#(X,Z))
             -->_1 sel#(0(),cons(X,Z)) -> c_4():5
             -->_1 sel#(s(X),cons(Y,Z)) -> c_5(sel#(X,Z)):3
          
          4:W:first#(0(),Z) -> c_1()
             
          
          5:W:sel#(0(),cons(X,Z)) -> c_4()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          5: sel#(0(),cons(X,Z)) -> c_4()
          4: first#(0(),Z) -> c_1()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          first#(s(X),cons(Y,Z)) -> c_2(first#(X,Z))
          from#(X) -> c_3(from#(s(X)))
          sel#(s(X),cons(Y,Z)) -> c_5(sel#(X,Z))
      - Signature:
          {first/2,from/1,sel/2,first#/2,from#/1,sel#/2} / {0/0,cons/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0,c_5/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {first#,from#,sel#} and constructors {0,cons,nil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE