* 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: InnermostRuleRemoval 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:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          g(0(),1()) -> s(0())
        All above mentioned rules can be savely removed.
* Step 3: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            0() -> 1()
            f(s(x)) -> f(g(x,x))
        - 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))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 4: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            0#() -> c_1()
            f#(s(x)) -> c_2(f#(g(x,x)),g#(x,x))
        - Weak TRS:
            0() -> 1()
            f(s(x)) -> f(g(x,x))
        - Signature:
            {0/0,f/1,g/2,0#/0,f#/1,g#/2} / {1/0,s/1,c_1/0,c_2/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {0#,f#,g#} and constructors {1,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          0#() -> c_1()
          f#(s(x)) -> c_2(f#(g(x,x)),g#(x,x))
* Step 5: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            0#() -> c_1()
            f#(s(x)) -> c_2(f#(g(x,x)),g#(x,x))
        - Signature:
            {0/0,f/1,g/2,0#/0,f#/1,g#/2} / {1/0,s/1,c_1/0,c_2/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {0#,f#,g#} and constructors {1,s}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:0#() -> c_1()
             
          
          2:S:f#(s(x)) -> c_2(f#(g(x,x)),g#(x,x))
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 6: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {0/0,f/1,g/2,0#/0,f#/1,g#/2} / {1/0,s/1,c_1/0,c_2/2}
        - 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))