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