MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            a__U11(X1,X2,X3) -> U11(X1,X2,X3)
            a__U11(tt(),M,N) -> a__U12(tt(),M,N)
            a__U12(X1,X2,X3) -> U12(X1,X2,X3)
            a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__plus(N,0()) -> mark(N)
            a__plus(N,s(M)) -> a__U11(tt(),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
            mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
        - Signature:
            {a__U11/3,a__U12/3,a__plus/2,mark/1} / {0/0,U11/3,U12/3,plus/2,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11,a__U12,a__plus,mark} and constructors {0,U11,U12
            ,plus,s,tt}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a__U11#(X1,X2,X3) -> c_1()
          a__U11#(tt(),M,N) -> c_2(a__U12#(tt(),M,N))
          a__U12#(X1,X2,X3) -> c_3()
          a__U12#(tt(),M,N) -> c_4(a__plus#(mark(N),mark(M)),mark#(N),mark#(M))
          a__plus#(N,0()) -> c_5(mark#(N))
          a__plus#(N,s(M)) -> c_6(a__U11#(tt(),M,N))
          a__plus#(X1,X2) -> c_7()
          mark#(0()) -> c_8()
          mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1))
          mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1))
          mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
          mark#(s(X)) -> c_12(mark#(X))
          mark#(tt()) -> c_13()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a__U11#(X1,X2,X3) -> c_1()
            a__U11#(tt(),M,N) -> c_2(a__U12#(tt(),M,N))
            a__U12#(X1,X2,X3) -> c_3()
            a__U12#(tt(),M,N) -> c_4(a__plus#(mark(N),mark(M)),mark#(N),mark#(M))
            a__plus#(N,0()) -> c_5(mark#(N))
            a__plus#(N,s(M)) -> c_6(a__U11#(tt(),M,N))
            a__plus#(X1,X2) -> c_7()
            mark#(0()) -> c_8()
            mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1))
            mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1))
            mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
            mark#(s(X)) -> c_12(mark#(X))
            mark#(tt()) -> c_13()
        - Weak TRS:
            a__U11(X1,X2,X3) -> U11(X1,X2,X3)
            a__U11(tt(),M,N) -> a__U12(tt(),M,N)
            a__U12(X1,X2,X3) -> U12(X1,X2,X3)
            a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__plus(N,0()) -> mark(N)
            a__plus(N,s(M)) -> a__U11(tt(),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
            mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
        - Signature:
            {a__U11/3,a__U12/3,a__plus/2,mark/1,a__U11#/3,a__U12#/3,a__plus#/2,mark#/1} / {0/0,U11/3,U12/3,plus/2,s/1
            ,tt/0,c_1/0,c_2/1,c_3/0,c_4/3,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/3,c_12/1,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11#,a__U12#,a__plus#,mark#} and constructors {0,U11
            ,U12,plus,s,tt}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,7,8,13}
        by application of
          Pre({1,3,7,8,13}) = {2,4,5,6,9,10,11,12}.
        Here rules are labelled as follows:
          1: a__U11#(X1,X2,X3) -> c_1()
          2: a__U11#(tt(),M,N) -> c_2(a__U12#(tt(),M,N))
          3: a__U12#(X1,X2,X3) -> c_3()
          4: a__U12#(tt(),M,N) -> c_4(a__plus#(mark(N),mark(M)),mark#(N),mark#(M))
          5: a__plus#(N,0()) -> c_5(mark#(N))
          6: a__plus#(N,s(M)) -> c_6(a__U11#(tt(),M,N))
          7: a__plus#(X1,X2) -> c_7()
          8: mark#(0()) -> c_8()
          9: mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1))
          10: mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1))
          11: mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
          12: mark#(s(X)) -> c_12(mark#(X))
          13: mark#(tt()) -> c_13()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            a__U11#(tt(),M,N) -> c_2(a__U12#(tt(),M,N))
            a__U12#(tt(),M,N) -> c_4(a__plus#(mark(N),mark(M)),mark#(N),mark#(M))
            a__plus#(N,0()) -> c_5(mark#(N))
            a__plus#(N,s(M)) -> c_6(a__U11#(tt(),M,N))
            mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1))
            mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1))
            mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
            mark#(s(X)) -> c_12(mark#(X))
        - Weak DPs:
            a__U11#(X1,X2,X3) -> c_1()
            a__U12#(X1,X2,X3) -> c_3()
            a__plus#(X1,X2) -> c_7()
            mark#(0()) -> c_8()
            mark#(tt()) -> c_13()
        - Weak TRS:
            a__U11(X1,X2,X3) -> U11(X1,X2,X3)
            a__U11(tt(),M,N) -> a__U12(tt(),M,N)
            a__U12(X1,X2,X3) -> U12(X1,X2,X3)
            a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__plus(N,0()) -> mark(N)
            a__plus(N,s(M)) -> a__U11(tt(),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
            mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
        - Signature:
            {a__U11/3,a__U12/3,a__plus/2,mark/1,a__U11#/3,a__U12#/3,a__plus#/2,mark#/1} / {0/0,U11/3,U12/3,plus/2,s/1
            ,tt/0,c_1/0,c_2/1,c_3/0,c_4/3,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/3,c_12/1,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11#,a__U12#,a__plus#,mark#} and constructors {0,U11
            ,U12,plus,s,tt}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:a__U11#(tt(),M,N) -> c_2(a__U12#(tt(),M,N))
             -->_1 a__U12#(tt(),M,N) -> c_4(a__plus#(mark(N),mark(M)),mark#(N),mark#(M)):2
             -->_1 a__U12#(X1,X2,X3) -> c_3():10
          
          2:S:a__U12#(tt(),M,N) -> c_4(a__plus#(mark(N),mark(M)),mark#(N),mark#(M))
             -->_3 mark#(s(X)) -> c_12(mark#(X)):8
             -->_2 mark#(s(X)) -> c_12(mark#(X)):8
             -->_3 mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):7
             -->_2 mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):7
             -->_3 mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1)):6
             -->_2 mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1)):6
             -->_3 mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1)):5
             -->_2 mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1)):5
             -->_1 a__plus#(N,s(M)) -> c_6(a__U11#(tt(),M,N)):4
             -->_1 a__plus#(N,0()) -> c_5(mark#(N)):3
             -->_3 mark#(tt()) -> c_13():13
             -->_2 mark#(tt()) -> c_13():13
             -->_3 mark#(0()) -> c_8():12
             -->_2 mark#(0()) -> c_8():12
             -->_1 a__plus#(X1,X2) -> c_7():11
          
          3:S:a__plus#(N,0()) -> c_5(mark#(N))
             -->_1 mark#(s(X)) -> c_12(mark#(X)):8
             -->_1 mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):7
             -->_1 mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1)):6
             -->_1 mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1)):5
             -->_1 mark#(tt()) -> c_13():13
             -->_1 mark#(0()) -> c_8():12
          
          4:S:a__plus#(N,s(M)) -> c_6(a__U11#(tt(),M,N))
             -->_1 a__U11#(X1,X2,X3) -> c_1():9
             -->_1 a__U11#(tt(),M,N) -> c_2(a__U12#(tt(),M,N)):1
          
          5:S:mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1))
             -->_2 mark#(s(X)) -> c_12(mark#(X)):8
             -->_2 mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):7
             -->_2 mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1)):6
             -->_2 mark#(tt()) -> c_13():13
             -->_2 mark#(0()) -> c_8():12
             -->_1 a__U11#(X1,X2,X3) -> c_1():9
             -->_2 mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1)):5
             -->_1 a__U11#(tt(),M,N) -> c_2(a__U12#(tt(),M,N)):1
          
          6:S:mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1))
             -->_2 mark#(s(X)) -> c_12(mark#(X)):8
             -->_2 mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):7
             -->_2 mark#(tt()) -> c_13():13
             -->_2 mark#(0()) -> c_8():12
             -->_1 a__U12#(X1,X2,X3) -> c_3():10
             -->_2 mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1)):6
             -->_2 mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1)):5
             -->_1 a__U12#(tt(),M,N) -> c_4(a__plus#(mark(N),mark(M)),mark#(N),mark#(M)):2
          
          7:S:mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
             -->_3 mark#(s(X)) -> c_12(mark#(X)):8
             -->_2 mark#(s(X)) -> c_12(mark#(X)):8
             -->_3 mark#(tt()) -> c_13():13
             -->_2 mark#(tt()) -> c_13():13
             -->_3 mark#(0()) -> c_8():12
             -->_2 mark#(0()) -> c_8():12
             -->_1 a__plus#(X1,X2) -> c_7():11
             -->_3 mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):7
             -->_2 mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):7
             -->_3 mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1)):6
             -->_2 mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1)):6
             -->_3 mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1)):5
             -->_2 mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1)):5
             -->_1 a__plus#(N,s(M)) -> c_6(a__U11#(tt(),M,N)):4
             -->_1 a__plus#(N,0()) -> c_5(mark#(N)):3
          
          8:S:mark#(s(X)) -> c_12(mark#(X))
             -->_1 mark#(tt()) -> c_13():13
             -->_1 mark#(0()) -> c_8():12
             -->_1 mark#(s(X)) -> c_12(mark#(X)):8
             -->_1 mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2)):7
             -->_1 mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1)):6
             -->_1 mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1)):5
          
          9:W:a__U11#(X1,X2,X3) -> c_1()
             
          
          10:W:a__U12#(X1,X2,X3) -> c_3()
             
          
          11:W:a__plus#(X1,X2) -> c_7()
             
          
          12:W:mark#(0()) -> c_8()
             
          
          13:W:mark#(tt()) -> c_13()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: a__U11#(X1,X2,X3) -> c_1()
          10: a__U12#(X1,X2,X3) -> c_3()
          11: a__plus#(X1,X2) -> c_7()
          12: mark#(0()) -> c_8()
          13: mark#(tt()) -> c_13()
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          a__U11#(tt(),M,N) -> c_2(a__U12#(tt(),M,N))
          a__U12#(tt(),M,N) -> c_4(a__plus#(mark(N),mark(M)),mark#(N),mark#(M))
          a__plus#(N,0()) -> c_5(mark#(N))
          a__plus#(N,s(M)) -> c_6(a__U11#(tt(),M,N))
          mark#(U11(X1,X2,X3)) -> c_9(a__U11#(mark(X1),X2,X3),mark#(X1))
          mark#(U12(X1,X2,X3)) -> c_10(a__U12#(mark(X1),X2,X3),mark#(X1))
          mark#(plus(X1,X2)) -> c_11(a__plus#(mark(X1),mark(X2)),mark#(X1),mark#(X2))
          mark#(s(X)) -> c_12(mark#(X))
      - Weak TRS:
          a__U11(X1,X2,X3) -> U11(X1,X2,X3)
          a__U11(tt(),M,N) -> a__U12(tt(),M,N)
          a__U12(X1,X2,X3) -> U12(X1,X2,X3)
          a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
          a__plus(N,0()) -> mark(N)
          a__plus(N,s(M)) -> a__U11(tt(),M,N)
          a__plus(X1,X2) -> plus(X1,X2)
          mark(0()) -> 0()
          mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
          mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
          mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
          mark(s(X)) -> s(mark(X))
          mark(tt()) -> tt()
      - Signature:
          {a__U11/3,a__U12/3,a__plus/2,mark/1,a__U11#/3,a__U12#/3,a__plus#/2,mark#/1} / {0/0,U11/3,U12/3,plus/2,s/1
          ,tt/0,c_1/0,c_2/1,c_3/0,c_4/3,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/3,c_12/1,c_13/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a__U11#,a__U12#,a__plus#,mark#} and constructors {0,U11
          ,U12,plus,s,tt}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE