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

WORST_CASE(?,O(1))