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