MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1} / {a/0,b/0,f/2,g/2,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__a,a__f,a__g,a__h,mark} and constructors {a,b,f,g,h}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a__a#() -> c_1()
          a__a#() -> c_2()
          a__f#(X,X) -> c_3(a__h#(a__a()),a__a#())
          a__f#(X1,X2) -> c_4()
          a__g#(X1,X2) -> c_5()
          a__g#(a(),X) -> c_6(a__f#(b(),X))
          a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
          a__h#(X) -> c_8()
          mark#(a()) -> c_9(a__a#())
          mark#(b()) -> c_10()
          mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
          mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
          mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a__a#() -> c_1()
            a__a#() -> c_2()
            a__f#(X,X) -> c_3(a__h#(a__a()),a__a#())
            a__f#(X1,X2) -> c_4()
            a__g#(X1,X2) -> c_5()
            a__g#(a(),X) -> c_6(a__f#(b(),X))
            a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
            a__h#(X) -> c_8()
            mark#(a()) -> c_9(a__a#())
            mark#(b()) -> c_10()
            mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
            mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
            mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
        - Weak TRS:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1,a__a#/0,a__f#/2,a__g#/2,a__h#/1,mark#/1} / {a/0,b/0,f/2,g/2,h/1,c_1/0
            ,c_2/0,c_3/2,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/1,c_10/0,c_11/2,c_12/2,c_13/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__a#,a__f#,a__g#,a__h#,mark#} and constructors {a,b,f,g
            ,h}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,4,5,8,10}
        by application of
          Pre({1,2,4,5,8,10}) = {3,6,7,9,11,12,13}.
        Here rules are labelled as follows:
          1: a__a#() -> c_1()
          2: a__a#() -> c_2()
          3: a__f#(X,X) -> c_3(a__h#(a__a()),a__a#())
          4: a__f#(X1,X2) -> c_4()
          5: a__g#(X1,X2) -> c_5()
          6: a__g#(a(),X) -> c_6(a__f#(b(),X))
          7: a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
          8: a__h#(X) -> c_8()
          9: mark#(a()) -> c_9(a__a#())
          10: mark#(b()) -> c_10()
          11: mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
          12: mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
          13: mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a__f#(X,X) -> c_3(a__h#(a__a()),a__a#())
            a__g#(a(),X) -> c_6(a__f#(b(),X))
            a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
            mark#(a()) -> c_9(a__a#())
            mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
            mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
            mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
        - Weak DPs:
            a__a#() -> c_1()
            a__a#() -> c_2()
            a__f#(X1,X2) -> c_4()
            a__g#(X1,X2) -> c_5()
            a__h#(X) -> c_8()
            mark#(b()) -> c_10()
        - Weak TRS:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1,a__a#/0,a__f#/2,a__g#/2,a__h#/1,mark#/1} / {a/0,b/0,f/2,g/2,h/1,c_1/0
            ,c_2/0,c_3/2,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/1,c_10/0,c_11/2,c_12/2,c_13/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__a#,a__f#,a__g#,a__h#,mark#} and constructors {a,b,f,g
            ,h}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {4}
        by application of
          Pre({4}) = {3,5,6,7}.
        Here rules are labelled as follows:
          1: a__f#(X,X) -> c_3(a__h#(a__a()),a__a#())
          2: a__g#(a(),X) -> c_6(a__f#(b(),X))
          3: a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
          4: mark#(a()) -> c_9(a__a#())
          5: mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
          6: mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
          7: mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
          8: a__a#() -> c_1()
          9: a__a#() -> c_2()
          10: a__f#(X1,X2) -> c_4()
          11: a__g#(X1,X2) -> c_5()
          12: a__h#(X) -> c_8()
          13: mark#(b()) -> c_10()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            a__f#(X,X) -> c_3(a__h#(a__a()),a__a#())
            a__g#(a(),X) -> c_6(a__f#(b(),X))
            a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
            mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
            mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
            mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
        - Weak DPs:
            a__a#() -> c_1()
            a__a#() -> c_2()
            a__f#(X1,X2) -> c_4()
            a__g#(X1,X2) -> c_5()
            a__h#(X) -> c_8()
            mark#(a()) -> c_9(a__a#())
            mark#(b()) -> c_10()
        - Weak TRS:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1,a__a#/0,a__f#/2,a__g#/2,a__h#/1,mark#/1} / {a/0,b/0,f/2,g/2,h/1,c_1/0
            ,c_2/0,c_3/2,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/1,c_10/0,c_11/2,c_12/2,c_13/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__a#,a__f#,a__g#,a__h#,mark#} and constructors {a,b,f,g
            ,h}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:a__f#(X,X) -> c_3(a__h#(a__a()),a__a#())
             -->_1 a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X)):3
             -->_1 a__h#(X) -> c_8():11
             -->_2 a__a#() -> c_2():8
             -->_2 a__a#() -> c_1():7
          
          2:S:a__g#(a(),X) -> c_6(a__f#(b(),X))
             -->_1 a__f#(X1,X2) -> c_4():9
             -->_1 a__f#(X,X) -> c_3(a__h#(a__a()),a__a#()):1
          
          3:S:a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
             -->_2 mark#(a()) -> c_9(a__a#()):12
             -->_2 mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X)):6
             -->_2 mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1)):4
             -->_2 mark#(b()) -> c_10():13
             -->_1 a__g#(X1,X2) -> c_5():10
             -->_1 a__g#(a(),X) -> c_6(a__f#(b(),X)):2
          
          4:S:mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
             -->_2 mark#(a()) -> c_9(a__a#()):12
             -->_2 mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X)):6
             -->_2 mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(b()) -> c_10():13
             -->_1 a__f#(X1,X2) -> c_4():9
             -->_2 mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1)):4
             -->_1 a__f#(X,X) -> c_3(a__h#(a__a()),a__a#()):1
          
          5:S:mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
             -->_2 mark#(a()) -> c_9(a__a#()):12
             -->_2 mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X)):6
             -->_2 mark#(b()) -> c_10():13
             -->_1 a__g#(X1,X2) -> c_5():10
             -->_2 mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1)):4
             -->_1 a__g#(a(),X) -> c_6(a__f#(b(),X)):2
          
          6:S:mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
             -->_2 mark#(a()) -> c_9(a__a#()):12
             -->_2 mark#(b()) -> c_10():13
             -->_1 a__h#(X) -> c_8():11
             -->_2 mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X)):6
             -->_2 mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1)):4
             -->_1 a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X)):3
          
          7:W:a__a#() -> c_1()
             
          
          8:W:a__a#() -> c_2()
             
          
          9:W:a__f#(X1,X2) -> c_4()
             
          
          10:W:a__g#(X1,X2) -> c_5()
             
          
          11:W:a__h#(X) -> c_8()
             
          
          12:W:mark#(a()) -> c_9(a__a#())
             -->_1 a__a#() -> c_2():8
             -->_1 a__a#() -> c_1():7
          
          13:W:mark#(b()) -> c_10()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: a__f#(X1,X2) -> c_4()
          10: a__g#(X1,X2) -> c_5()
          11: a__h#(X) -> c_8()
          13: mark#(b()) -> c_10()
          12: mark#(a()) -> c_9(a__a#())
          7: a__a#() -> c_1()
          8: a__a#() -> c_2()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            a__f#(X,X) -> c_3(a__h#(a__a()),a__a#())
            a__g#(a(),X) -> c_6(a__f#(b(),X))
            a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
            mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
            mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
            mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
        - Weak TRS:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1,a__a#/0,a__f#/2,a__g#/2,a__h#/1,mark#/1} / {a/0,b/0,f/2,g/2,h/1,c_1/0
            ,c_2/0,c_3/2,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/1,c_10/0,c_11/2,c_12/2,c_13/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__a#,a__f#,a__g#,a__h#,mark#} and constructors {a,b,f,g
            ,h}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:a__f#(X,X) -> c_3(a__h#(a__a()),a__a#())
             -->_1 a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X)):3
          
          2:S:a__g#(a(),X) -> c_6(a__f#(b(),X))
             -->_1 a__f#(X,X) -> c_3(a__h#(a__a()),a__a#()):1
          
          3:S:a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
             -->_2 mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X)):6
             -->_2 mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1)):4
             -->_1 a__g#(a(),X) -> c_6(a__f#(b(),X)):2
          
          4:S:mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
             -->_2 mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X)):6
             -->_2 mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1)):4
             -->_1 a__f#(X,X) -> c_3(a__h#(a__a()),a__a#()):1
          
          5:S:mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
             -->_2 mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X)):6
             -->_2 mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1)):4
             -->_1 a__g#(a(),X) -> c_6(a__f#(b(),X)):2
          
          6:S:mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
             -->_2 mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X)):6
             -->_2 mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1)):4
             -->_1 a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X)):3
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          a__f#(X,X) -> c_3(a__h#(a__a()))
* Step 6: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            a__f#(X,X) -> c_3(a__h#(a__a()))
            a__g#(a(),X) -> c_6(a__f#(b(),X))
            a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
            mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
            mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
            mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
        - Weak TRS:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1,a__a#/0,a__f#/2,a__g#/2,a__h#/1,mark#/1} / {a/0,b/0,f/2,g/2,h/1,c_1/0
            ,c_2/0,c_3/1,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/1,c_10/0,c_11/2,c_12/2,c_13/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__a#,a__f#,a__g#,a__h#,mark#} and constructors {a,b,f,g
            ,h}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            uargs(a__f) = {1},
            uargs(a__g) = {1},
            uargs(a__h) = {1},
            uargs(a__f#) = {1},
            uargs(a__g#) = {1},
            uargs(a__h#) = {1},
            uargs(c_3) = {1},
            uargs(c_6) = {1},
            uargs(c_7) = {1,2},
            uargs(c_11) = {1,2},
            uargs(c_12) = {1,2},
            uargs(c_13) = {1,2}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(a) = [0]                  
             p(a__a) = [0]                  
             p(a__f) = [1] x1 + [0]         
             p(a__g) = [1] x1 + [0]         
             p(a__h) = [1] x1 + [0]         
                p(b) = [0]                  
                p(f) = [0]                  
                p(g) = [0]                  
                p(h) = [0]                  
             p(mark) = [0]                  
            p(a__a#) = [0]                  
            p(a__f#) = [1] x1 + [6]         
            p(a__g#) = [1] x1 + [0]         
            p(a__h#) = [1] x1 + [1]         
            p(mark#) = [3]                  
              p(c_1) = [0]                  
              p(c_2) = [0]                  
              p(c_3) = [1] x1 + [4]         
              p(c_4) = [0]                  
              p(c_5) = [0]                  
              p(c_6) = [1] x1 + [0]         
              p(c_7) = [1] x1 + [1] x2 + [1]
              p(c_8) = [0]                  
              p(c_9) = [0]                  
             p(c_10) = [0]                  
             p(c_11) = [1] x1 + [1] x2 + [0]
             p(c_12) = [1] x1 + [1] x2 + [0]
             p(c_13) = [1] x1 + [1] x2 + [7]
          
          Following rules are strictly oriented:
          a__f#(X,X) = [1] X + [6]       
                     > [5]               
                     = c_3(a__h#(a__a()))
          
          
          Following rules are (at-least) weakly oriented:
             a__g#(a(),X) =  [0]                               
                          >= [6]                               
                          =  c_6(a__f#(b(),X))                 
          
                 a__h#(X) =  [1] X + [1]                       
                          >= [4]                               
                          =  c_7(a__g#(mark(X),X),mark#(X))    
          
          mark#(f(X1,X2)) =  [3]                               
                          >= [9]                               
                          =  c_11(a__f#(mark(X1),X2),mark#(X1))
          
          mark#(g(X1,X2)) =  [3]                               
                          >= [3]                               
                          =  c_12(a__g#(mark(X1),X2),mark#(X1))
          
              mark#(h(X)) =  [3]                               
                          >= [11]                              
                          =  c_13(a__h#(mark(X)),mark#(X))     
          
                   a__a() =  [0]                               
                          >= [0]                               
                          =  a()                               
          
                   a__a() =  [0]                               
                          >= [0]                               
                          =  b()                               
          
                a__f(X,X) =  [1] X + [0]                       
                          >= [0]                               
                          =  a__h(a__a())                      
          
              a__f(X1,X2) =  [1] X1 + [0]                      
                          >= [0]                               
                          =  f(X1,X2)                          
          
              a__g(X1,X2) =  [1] X1 + [0]                      
                          >= [0]                               
                          =  g(X1,X2)                          
          
              a__g(a(),X) =  [0]                               
                          >= [0]                               
                          =  a__f(b(),X)                       
          
                  a__h(X) =  [1] X + [0]                       
                          >= [0]                               
                          =  a__g(mark(X),X)                   
          
                  a__h(X) =  [1] X + [0]                       
                          >= [0]                               
                          =  h(X)                              
          
                mark(a()) =  [0]                               
                          >= [0]                               
                          =  a__a()                            
          
                mark(b()) =  [0]                               
                          >= [0]                               
                          =  b()                               
          
           mark(f(X1,X2)) =  [0]                               
                          >= [0]                               
                          =  a__f(mark(X1),X2)                 
          
           mark(g(X1,X2)) =  [0]                               
                          >= [0]                               
                          =  a__g(mark(X1),X2)                 
          
               mark(h(X)) =  [0]                               
                          >= [0]                               
                          =  a__h(mark(X))                     
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 7: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            a__g#(a(),X) -> c_6(a__f#(b(),X))
            a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
            mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
            mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
            mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
        - Weak DPs:
            a__f#(X,X) -> c_3(a__h#(a__a()))
        - Weak TRS:
            a__a() -> a()
            a__a() -> b()
            a__f(X,X) -> a__h(a__a())
            a__f(X1,X2) -> f(X1,X2)
            a__g(X1,X2) -> g(X1,X2)
            a__g(a(),X) -> a__f(b(),X)
            a__h(X) -> a__g(mark(X),X)
            a__h(X) -> h(X)
            mark(a()) -> a__a()
            mark(b()) -> b()
            mark(f(X1,X2)) -> a__f(mark(X1),X2)
            mark(g(X1,X2)) -> a__g(mark(X1),X2)
            mark(h(X)) -> a__h(mark(X))
        - Signature:
            {a__a/0,a__f/2,a__g/2,a__h/1,mark/1,a__a#/0,a__f#/2,a__g#/2,a__h#/1,mark#/1} / {a/0,b/0,f/2,g/2,h/1,c_1/0
            ,c_2/0,c_3/1,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/1,c_10/0,c_11/2,c_12/2,c_13/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__a#,a__f#,a__g#,a__h#,mark#} and constructors {a,b,f,g
            ,h}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            uargs(a__f) = {1},
            uargs(a__g) = {1},
            uargs(a__h) = {1},
            uargs(a__f#) = {1},
            uargs(a__g#) = {1},
            uargs(a__h#) = {1},
            uargs(c_3) = {1},
            uargs(c_6) = {1},
            uargs(c_7) = {1,2},
            uargs(c_11) = {1,2},
            uargs(c_12) = {1,2},
            uargs(c_13) = {1,2}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(a) = [0]                  
             p(a__a) = [0]                  
             p(a__f) = [1] x1 + [0]         
             p(a__g) = [1] x1 + [0]         
             p(a__h) = [1] x1 + [0]         
                p(b) = [0]                  
                p(f) = [0]                  
                p(g) = [0]                  
                p(h) = [0]                  
             p(mark) = [0]                  
            p(a__a#) = [0]                  
            p(a__f#) = [1] x1 + [0]         
            p(a__g#) = [1] x1 + [2]         
            p(a__h#) = [1] x1 + [0]         
            p(mark#) = [1]                  
              p(c_1) = [4]                  
              p(c_2) = [1]                  
              p(c_3) = [1] x1 + [0]         
              p(c_4) = [0]                  
              p(c_5) = [0]                  
              p(c_6) = [1] x1 + [0]         
              p(c_7) = [1] x1 + [1] x2 + [0]
              p(c_8) = [0]                  
              p(c_9) = [0]                  
             p(c_10) = [0]                  
             p(c_11) = [1] x1 + [1] x2 + [7]
             p(c_12) = [1] x1 + [1] x2 + [0]
             p(c_13) = [1] x1 + [1] x2 + [0]
          
          Following rules are strictly oriented:
          a__g#(a(),X) = [2]              
                       > [0]              
                       = c_6(a__f#(b(),X))
          
          
          Following rules are (at-least) weakly oriented:
               a__f#(X,X) =  [1] X + [0]                       
                          >= [0]                               
                          =  c_3(a__h#(a__a()))                
          
                 a__h#(X) =  [1] X + [0]                       
                          >= [3]                               
                          =  c_7(a__g#(mark(X),X),mark#(X))    
          
          mark#(f(X1,X2)) =  [1]                               
                          >= [8]                               
                          =  c_11(a__f#(mark(X1),X2),mark#(X1))
          
          mark#(g(X1,X2)) =  [1]                               
                          >= [3]                               
                          =  c_12(a__g#(mark(X1),X2),mark#(X1))
          
              mark#(h(X)) =  [1]                               
                          >= [1]                               
                          =  c_13(a__h#(mark(X)),mark#(X))     
          
                   a__a() =  [0]                               
                          >= [0]                               
                          =  a()                               
          
                   a__a() =  [0]                               
                          >= [0]                               
                          =  b()                               
          
                a__f(X,X) =  [1] X + [0]                       
                          >= [0]                               
                          =  a__h(a__a())                      
          
              a__f(X1,X2) =  [1] X1 + [0]                      
                          >= [0]                               
                          =  f(X1,X2)                          
          
              a__g(X1,X2) =  [1] X1 + [0]                      
                          >= [0]                               
                          =  g(X1,X2)                          
          
              a__g(a(),X) =  [0]                               
                          >= [0]                               
                          =  a__f(b(),X)                       
          
                  a__h(X) =  [1] X + [0]                       
                          >= [0]                               
                          =  a__g(mark(X),X)                   
          
                  a__h(X) =  [1] X + [0]                       
                          >= [0]                               
                          =  h(X)                              
          
                mark(a()) =  [0]                               
                          >= [0]                               
                          =  a__a()                            
          
                mark(b()) =  [0]                               
                          >= [0]                               
                          =  b()                               
          
           mark(f(X1,X2)) =  [0]                               
                          >= [0]                               
                          =  a__f(mark(X1),X2)                 
          
           mark(g(X1,X2)) =  [0]                               
                          >= [0]                               
                          =  a__g(mark(X1),X2)                 
          
               mark(h(X)) =  [0]                               
                          >= [0]                               
                          =  a__h(mark(X))                     
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 8: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          a__h#(X) -> c_7(a__g#(mark(X),X),mark#(X))
          mark#(f(X1,X2)) -> c_11(a__f#(mark(X1),X2),mark#(X1))
          mark#(g(X1,X2)) -> c_12(a__g#(mark(X1),X2),mark#(X1))
          mark#(h(X)) -> c_13(a__h#(mark(X)),mark#(X))
      - Weak DPs:
          a__f#(X,X) -> c_3(a__h#(a__a()))
          a__g#(a(),X) -> c_6(a__f#(b(),X))
      - Weak TRS:
          a__a() -> a()
          a__a() -> b()
          a__f(X,X) -> a__h(a__a())
          a__f(X1,X2) -> f(X1,X2)
          a__g(X1,X2) -> g(X1,X2)
          a__g(a(),X) -> a__f(b(),X)
          a__h(X) -> a__g(mark(X),X)
          a__h(X) -> h(X)
          mark(a()) -> a__a()
          mark(b()) -> b()
          mark(f(X1,X2)) -> a__f(mark(X1),X2)
          mark(g(X1,X2)) -> a__g(mark(X1),X2)
          mark(h(X)) -> a__h(mark(X))
      - Signature:
          {a__a/0,a__f/2,a__g/2,a__h/1,mark/1,a__a#/0,a__f#/2,a__g#/2,a__h#/1,mark#/1} / {a/0,b/0,f/2,g/2,h/1,c_1/0
          ,c_2/0,c_3/1,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/1,c_10/0,c_11/2,c_12/2,c_13/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a__a#,a__f#,a__g#,a__h#,mark#} and constructors {a,b,f,g
          ,h}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE