MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            a__after(X1,X2) -> after(X1,X2)
            a__after(0(),XS) -> mark(XS)
            a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            mark(0()) -> 0()
            mark(after(X1,X2)) -> a__after(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__after/2,a__from/1,mark/1} / {0/0,after/2,cons/2,from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__after,a__from,mark} and constructors {0,after,cons
            ,from,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a__after#(X1,X2) -> c_1()
          a__after#(0(),XS) -> c_2(mark#(XS))
          a__after#(s(N),cons(X,XS)) -> c_3(a__after#(mark(N),mark(XS)),mark#(N),mark#(XS))
          a__from#(X) -> c_4(mark#(X))
          a__from#(X) -> c_5()
          mark#(0()) -> c_6()
          mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
          mark#(cons(X1,X2)) -> c_8(mark#(X1))
          mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X))
          mark#(s(X)) -> c_10(mark#(X))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a__after#(X1,X2) -> c_1()
            a__after#(0(),XS) -> c_2(mark#(XS))
            a__after#(s(N),cons(X,XS)) -> c_3(a__after#(mark(N),mark(XS)),mark#(N),mark#(XS))
            a__from#(X) -> c_4(mark#(X))
            a__from#(X) -> c_5()
            mark#(0()) -> c_6()
            mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
            mark#(cons(X1,X2)) -> c_8(mark#(X1))
            mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X))
            mark#(s(X)) -> c_10(mark#(X))
        - Weak TRS:
            a__after(X1,X2) -> after(X1,X2)
            a__after(0(),XS) -> mark(XS)
            a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            mark(0()) -> 0()
            mark(after(X1,X2)) -> a__after(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__after/2,a__from/1,mark/1,a__after#/2,a__from#/1,mark#/1} / {0/0,after/2,cons/2,from/1,s/1,c_1/0,c_2/1
            ,c_3/3,c_4/1,c_5/0,c_6/0,c_7/3,c_8/1,c_9/2,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__after#,a__from#,mark#} and constructors {0,after,cons
            ,from,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,5,6}
        by application of
          Pre({1,5,6}) = {2,3,4,7,8,9,10}.
        Here rules are labelled as follows:
          1: a__after#(X1,X2) -> c_1()
          2: a__after#(0(),XS) -> c_2(mark#(XS))
          3: a__after#(s(N),cons(X,XS)) -> c_3(a__after#(mark(N),mark(XS)),mark#(N),mark#(XS))
          4: a__from#(X) -> c_4(mark#(X))
          5: a__from#(X) -> c_5()
          6: mark#(0()) -> c_6()
          7: mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
          8: mark#(cons(X1,X2)) -> c_8(mark#(X1))
          9: mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X))
          10: mark#(s(X)) -> c_10(mark#(X))
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            a__after#(0(),XS) -> c_2(mark#(XS))
            a__after#(s(N),cons(X,XS)) -> c_3(a__after#(mark(N),mark(XS)),mark#(N),mark#(XS))
            a__from#(X) -> c_4(mark#(X))
            mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
            mark#(cons(X1,X2)) -> c_8(mark#(X1))
            mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X))
            mark#(s(X)) -> c_10(mark#(X))
        - Weak DPs:
            a__after#(X1,X2) -> c_1()
            a__from#(X) -> c_5()
            mark#(0()) -> c_6()
        - Weak TRS:
            a__after(X1,X2) -> after(X1,X2)
            a__after(0(),XS) -> mark(XS)
            a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            mark(0()) -> 0()
            mark(after(X1,X2)) -> a__after(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__after/2,a__from/1,mark/1,a__after#/2,a__from#/1,mark#/1} / {0/0,after/2,cons/2,from/1,s/1,c_1/0,c_2/1
            ,c_3/3,c_4/1,c_5/0,c_6/0,c_7/3,c_8/1,c_9/2,c_10/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__after#,a__from#,mark#} and constructors {0,after,cons
            ,from,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:a__after#(0(),XS) -> c_2(mark#(XS))
             -->_1 mark#(s(X)) -> c_10(mark#(X)):7
             -->_1 mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X)):6
             -->_1 mark#(cons(X1,X2)) -> c_8(mark#(X1)):5
             -->_1 mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):4
             -->_1 mark#(0()) -> c_6():10
          
          2:S:a__after#(s(N),cons(X,XS)) -> c_3(a__after#(mark(N),mark(XS)),mark#(N),mark#(XS))
             -->_3 mark#(s(X)) -> c_10(mark#(X)):7
             -->_2 mark#(s(X)) -> c_10(mark#(X)):7
             -->_3 mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X)):6
             -->_2 mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X)):6
             -->_3 mark#(cons(X1,X2)) -> c_8(mark#(X1)):5
             -->_2 mark#(cons(X1,X2)) -> c_8(mark#(X1)):5
             -->_3 mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):4
             -->_2 mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):4
             -->_3 mark#(0()) -> c_6():10
             -->_2 mark#(0()) -> c_6():10
             -->_1 a__after#(X1,X2) -> c_1():8
             -->_1 a__after#(s(N),cons(X,XS)) -> c_3(a__after#(mark(N),mark(XS)),mark#(N),mark#(XS)):2
             -->_1 a__after#(0(),XS) -> c_2(mark#(XS)):1
          
          3:S:a__from#(X) -> c_4(mark#(X))
             -->_1 mark#(s(X)) -> c_10(mark#(X)):7
             -->_1 mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X)):6
             -->_1 mark#(cons(X1,X2)) -> c_8(mark#(X1)):5
             -->_1 mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):4
             -->_1 mark#(0()) -> c_6():10
          
          4:S:mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
             -->_3 mark#(s(X)) -> c_10(mark#(X)):7
             -->_2 mark#(s(X)) -> c_10(mark#(X)):7
             -->_3 mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X)):6
             -->_2 mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X)):6
             -->_3 mark#(cons(X1,X2)) -> c_8(mark#(X1)):5
             -->_2 mark#(cons(X1,X2)) -> c_8(mark#(X1)):5
             -->_3 mark#(0()) -> c_6():10
             -->_2 mark#(0()) -> c_6():10
             -->_1 a__after#(X1,X2) -> c_1():8
             -->_3 mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):4
             -->_2 mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):4
             -->_1 a__after#(s(N),cons(X,XS)) -> c_3(a__after#(mark(N),mark(XS)),mark#(N),mark#(XS)):2
             -->_1 a__after#(0(),XS) -> c_2(mark#(XS)):1
          
          5:S:mark#(cons(X1,X2)) -> c_8(mark#(X1))
             -->_1 mark#(s(X)) -> c_10(mark#(X)):7
             -->_1 mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X)):6
             -->_1 mark#(0()) -> c_6():10
             -->_1 mark#(cons(X1,X2)) -> c_8(mark#(X1)):5
             -->_1 mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):4
          
          6:S:mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X))
             -->_2 mark#(s(X)) -> c_10(mark#(X)):7
             -->_2 mark#(0()) -> c_6():10
             -->_1 a__from#(X) -> c_5():9
             -->_2 mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X)):6
             -->_2 mark#(cons(X1,X2)) -> c_8(mark#(X1)):5
             -->_2 mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):4
             -->_1 a__from#(X) -> c_4(mark#(X)):3
          
          7:S:mark#(s(X)) -> c_10(mark#(X))
             -->_1 mark#(0()) -> c_6():10
             -->_1 mark#(s(X)) -> c_10(mark#(X)):7
             -->_1 mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X)):6
             -->_1 mark#(cons(X1,X2)) -> c_8(mark#(X1)):5
             -->_1 mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):4
          
          8:W:a__after#(X1,X2) -> c_1()
             
          
          9:W:a__from#(X) -> c_5()
             
          
          10:W:mark#(0()) -> c_6()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: a__after#(X1,X2) -> c_1()
          9: a__from#(X) -> c_5()
          10: mark#(0()) -> c_6()
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          a__after#(0(),XS) -> c_2(mark#(XS))
          a__after#(s(N),cons(X,XS)) -> c_3(a__after#(mark(N),mark(XS)),mark#(N),mark#(XS))
          a__from#(X) -> c_4(mark#(X))
          mark#(after(X1,X2)) -> c_7(a__after#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
          mark#(cons(X1,X2)) -> c_8(mark#(X1))
          mark#(from(X)) -> c_9(a__from#(mark(X)),mark#(X))
          mark#(s(X)) -> c_10(mark#(X))
      - Weak TRS:
          a__after(X1,X2) -> after(X1,X2)
          a__after(0(),XS) -> mark(XS)
          a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS))
          a__from(X) -> cons(mark(X),from(s(X)))
          a__from(X) -> from(X)
          mark(0()) -> 0()
          mark(after(X1,X2)) -> a__after(mark(X1),mark(X2))
          mark(cons(X1,X2)) -> cons(mark(X1),X2)
          mark(from(X)) -> a__from(mark(X))
          mark(s(X)) -> s(mark(X))
      - Signature:
          {a__after/2,a__from/1,mark/1,a__after#/2,a__from#/1,mark#/1} / {0/0,after/2,cons/2,from/1,s/1,c_1/0,c_2/1
          ,c_3/3,c_4/1,c_5/0,c_6/0,c_7/3,c_8/1,c_9/2,c_10/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a__after#,a__from#,mark#} and constructors {0,after,cons
          ,from,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE