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