* Step 1: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            +(x,0()) -> x
            +(x,i(x)) -> 0()
        - Signature:
            {+/2} / {0/0,i/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+} and constructors {0,i}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          +#(x,0()) -> c_1()
          +#(x,i(x)) -> c_2()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            +#(x,0()) -> c_1()
            +#(x,i(x)) -> c_2()
        - Weak TRS:
            +(x,0()) -> x
            +(x,i(x)) -> 0()
        - Signature:
            {+/2,+#/2} / {0/0,i/1,c_1/0,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#} and constructors {0,i}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          +#(x,0()) -> c_1()
          +#(x,i(x)) -> c_2()
* Step 3: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            +#(x,0()) -> c_1()
            +#(x,i(x)) -> c_2()
        - Signature:
            {+/2,+#/2} / {0/0,i/1,c_1/0,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#} and constructors {0,i}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:+#(x,0()) -> c_1()
             
          
          2:S:+#(x,i(x)) -> c_2()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {+/2,+#/2} / {0/0,i/1,c_1/0,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#} and constructors {0,i}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))