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