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

WORST_CASE(?,O(1))