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