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

WORST_CASE(?,O(1))