MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            f(0(),x2) -> 0()
            f(S(x),0()) -> 0()
            f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x))
            g(0(),x2) -> 0()
            g(S(x),0()) -> 0()
            g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x'))))
            h(0(),0()) -> 0()
            h(0(),S(x)) -> h(0(),x)
            h(S(x),x2) -> h(x,x2)
        - Signature:
            {f/2,g/2,h/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,h} and constructors {0,S}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          f#(0(),x2) -> c_1()
          f#(S(x),0()) -> c_2()
          f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x))
          g#(0(),x2) -> c_4()
          g#(S(x),0()) -> c_5()
          g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x'))))
          h#(0(),0()) -> c_7()
          h#(0(),S(x)) -> c_8(h#(0(),x))
          h#(S(x),x2) -> c_9(h#(x,x2))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(0(),x2) -> c_1()
            f#(S(x),0()) -> c_2()
            f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x))
            g#(0(),x2) -> c_4()
            g#(S(x),0()) -> c_5()
            g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x'))))
            h#(0(),0()) -> c_7()
            h#(0(),S(x)) -> c_8(h#(0(),x))
            h#(S(x),x2) -> c_9(h#(x,x2))
        - Weak TRS:
            f(0(),x2) -> 0()
            f(S(x),0()) -> 0()
            f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x))
            g(0(),x2) -> 0()
            g(S(x),0()) -> 0()
            g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x'))))
            h(0(),0()) -> 0()
            h(0(),S(x)) -> h(0(),x)
            h(S(x),x2) -> h(x,x2)
        - Signature:
            {f/2,g/2,h/2,f#/2,g#/2,h#/2} / {0/0,S/1,c_1/0,c_2/0,c_3/3,c_4/0,c_5/0,c_6/3,c_7/0,c_8/1,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#,h#} and constructors {0,S}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          f(S(x),0()) -> 0()
          f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x))
          g(0(),x2) -> 0()
          g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x'))))
          h(0(),0()) -> 0()
          h(0(),S(x)) -> h(0(),x)
          h(S(x),x2) -> h(x,x2)
          f#(0(),x2) -> c_1()
          f#(S(x),0()) -> c_2()
          f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x))
          g#(0(),x2) -> c_4()
          g#(S(x),0()) -> c_5()
          g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x'))))
          h#(0(),0()) -> c_7()
          h#(0(),S(x)) -> c_8(h#(0(),x))
          h#(S(x),x2) -> c_9(h#(x,x2))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(0(),x2) -> c_1()
            f#(S(x),0()) -> c_2()
            f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x))
            g#(0(),x2) -> c_4()
            g#(S(x),0()) -> c_5()
            g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x'))))
            h#(0(),0()) -> c_7()
            h#(0(),S(x)) -> c_8(h#(0(),x))
            h#(S(x),x2) -> c_9(h#(x,x2))
        - Weak TRS:
            f(S(x),0()) -> 0()
            f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x))
            g(0(),x2) -> 0()
            g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x'))))
            h(0(),0()) -> 0()
            h(0(),S(x)) -> h(0(),x)
            h(S(x),x2) -> h(x,x2)
        - Signature:
            {f/2,g/2,h/2,f#/2,g#/2,h#/2} / {0/0,S/1,c_1/0,c_2/0,c_3/3,c_4/0,c_5/0,c_6/3,c_7/0,c_8/1,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#,h#} and constructors {0,S}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,4,5,7}
        by application of
          Pre({1,2,4,5,7}) = {3,6,8,9}.
        Here rules are labelled as follows:
          1: f#(0(),x2) -> c_1()
          2: f#(S(x),0()) -> c_2()
          3: f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x))
          4: g#(0(),x2) -> c_4()
          5: g#(S(x),0()) -> c_5()
          6: g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x'))))
          7: h#(0(),0()) -> c_7()
          8: h#(0(),S(x)) -> c_8(h#(0(),x))
          9: h#(S(x),x2) -> c_9(h#(x,x2))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x))
            g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x'))))
            h#(0(),S(x)) -> c_8(h#(0(),x))
            h#(S(x),x2) -> c_9(h#(x,x2))
        - Weak DPs:
            f#(0(),x2) -> c_1()
            f#(S(x),0()) -> c_2()
            g#(0(),x2) -> c_4()
            g#(S(x),0()) -> c_5()
            h#(0(),0()) -> c_7()
        - Weak TRS:
            f(S(x),0()) -> 0()
            f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x))
            g(0(),x2) -> 0()
            g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x'))))
            h(0(),0()) -> 0()
            h(0(),S(x)) -> h(0(),x)
            h(S(x),x2) -> h(x,x2)
        - Signature:
            {f/2,g/2,h/2,f#/2,g#/2,h#/2} / {0/0,S/1,c_1/0,c_2/0,c_3/3,c_4/0,c_5/0,c_6/3,c_7/0,c_8/1,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#,h#} and constructors {0,S}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x))
             -->_1 h#(S(x),x2) -> c_9(h#(x,x2)):4
             -->_1 h#(0(),S(x)) -> c_8(h#(0(),x)):3
             -->_2 g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x')))):2
             -->_1 h#(0(),0()) -> c_7():9
             -->_2 g#(0(),x2) -> c_4():7
             -->_3 f#(S(x),0()) -> c_2():6
             -->_3 f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x)):1
          
          2:S:g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x'))))
             -->_1 h#(S(x),x2) -> c_9(h#(x,x2)):4
             -->_1 h#(0(),S(x)) -> c_8(h#(0(),x)):3
             -->_1 h#(0(),0()) -> c_7():9
             -->_3 g#(0(),x2) -> c_4():7
             -->_3 g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x')))):2
             -->_2 f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x)):1
          
          3:S:h#(0(),S(x)) -> c_8(h#(0(),x))
             -->_1 h#(0(),0()) -> c_7():9
             -->_1 h#(0(),S(x)) -> c_8(h#(0(),x)):3
          
          4:S:h#(S(x),x2) -> c_9(h#(x,x2))
             -->_1 h#(0(),0()) -> c_7():9
             -->_1 h#(S(x),x2) -> c_9(h#(x,x2)):4
             -->_1 h#(0(),S(x)) -> c_8(h#(0(),x)):3
          
          5:W:f#(0(),x2) -> c_1()
             
          
          6:W:f#(S(x),0()) -> c_2()
             
          
          7:W:g#(0(),x2) -> c_4()
             
          
          8:W:g#(S(x),0()) -> c_5()
             
          
          9:W:h#(0(),0()) -> c_7()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: g#(S(x),0()) -> c_5()
          5: f#(0(),x2) -> c_1()
          6: f#(S(x),0()) -> c_2()
          7: g#(0(),x2) -> c_4()
          9: h#(0(),0()) -> c_7()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(S(x'),S(x)) -> c_3(h#(g(x',S(x)),f(S(S(x')),x)),g#(x',S(x)),f#(S(S(x')),x))
          g#(S(x),S(x')) -> c_6(h#(f(S(x),S(x')),g(x,S(S(x')))),f#(S(x),S(x')),g#(x,S(S(x'))))
          h#(0(),S(x)) -> c_8(h#(0(),x))
          h#(S(x),x2) -> c_9(h#(x,x2))
      - Weak TRS:
          f(S(x),0()) -> 0()
          f(S(x'),S(x)) -> h(g(x',S(x)),f(S(S(x')),x))
          g(0(),x2) -> 0()
          g(S(x),S(x')) -> h(f(S(x),S(x')),g(x,S(S(x'))))
          h(0(),0()) -> 0()
          h(0(),S(x)) -> h(0(),x)
          h(S(x),x2) -> h(x,x2)
      - Signature:
          {f/2,g/2,h/2,f#/2,g#/2,h#/2} / {0/0,S/1,c_1/0,c_2/0,c_3/3,c_4/0,c_5/0,c_6/3,c_7/0,c_8/1,c_9/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {f#,g#,h#} and constructors {0,S}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE