WORST_CASE(?,O(1))
* Step 1: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(k(a()),k(b()),X) -> f(X,X,X)
            g(X) -> u(h(X),h(X),X)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(Y),X) -> k(Y)
        - Signature:
            {f/3,g/1,h/1,u/3} / {a/0,b/0,c/1,d/0,k/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,h,u} and constructors {a,b,c,d,k}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          f#(k(a()),k(b()),X) -> c_1(f#(X,X,X))
          g#(X) -> c_2(u#(h(X),h(X),X),h#(X),h#(X))
          h#(d()) -> c_3()
          h#(d()) -> c_4()
          u#(d(),c(Y),X) -> c_5()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(k(a()),k(b()),X) -> c_1(f#(X,X,X))
            g#(X) -> c_2(u#(h(X),h(X),X),h#(X),h#(X))
            h#(d()) -> c_3()
            h#(d()) -> c_4()
            u#(d(),c(Y),X) -> c_5()
        - Weak TRS:
            f(k(a()),k(b()),X) -> f(X,X,X)
            g(X) -> u(h(X),h(X),X)
            h(d()) -> c(a())
            h(d()) -> c(b())
            u(d(),c(Y),X) -> k(Y)
        - Signature:
            {f/3,g/1,h/1,u/3,f#/3,g#/1,h#/1,u#/3} / {a/0,b/0,c/1,d/0,k/1,c_1/1,c_2/3,c_3/0,c_4/0,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#,h#,u#} and constructors {a,b,c,d,k}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          h(d()) -> c(a())
          h(d()) -> c(b())
          f#(k(a()),k(b()),X) -> c_1(f#(X,X,X))
          g#(X) -> c_2(u#(h(X),h(X),X),h#(X),h#(X))
          h#(d()) -> c_3()
          h#(d()) -> c_4()
          u#(d(),c(Y),X) -> c_5()
* Step 3: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(k(a()),k(b()),X) -> c_1(f#(X,X,X))
            g#(X) -> c_2(u#(h(X),h(X),X),h#(X),h#(X))
            h#(d()) -> c_3()
            h#(d()) -> c_4()
            u#(d(),c(Y),X) -> c_5()
        - Weak TRS:
            h(d()) -> c(a())
            h(d()) -> c(b())
        - Signature:
            {f/3,g/1,h/1,u/3,f#/3,g#/1,h#/1,u#/3} / {a/0,b/0,c/1,d/0,k/1,c_1/1,c_2/3,c_3/0,c_4/0,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#,h#,u#} and constructors {a,b,c,d,k}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:f#(k(a()),k(b()),X) -> c_1(f#(X,X,X))
             
          
          2:S:g#(X) -> c_2(u#(h(X),h(X),X),h#(X),h#(X))
             -->_1 u#(d(),c(Y),X) -> c_5():5
             -->_3 h#(d()) -> c_4():4
             -->_2 h#(d()) -> c_4():4
             -->_3 h#(d()) -> c_3():3
             -->_2 h#(d()) -> c_3():3
          
          3:S:h#(d()) -> c_3()
             
          
          4:S:h#(d()) -> c_4()
             
          
          5:S:u#(d(),c(Y),X) -> c_5()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            h(d()) -> c(a())
            h(d()) -> c(b())
        - Signature:
            {f/3,g/1,h/1,u/3,f#/3,g#/1,h#/1,u#/3} / {a/0,b/0,c/1,d/0,k/1,c_1/1,c_2/3,c_3/0,c_4/0,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#,h#,u#} and constructors {a,b,c,d,k}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))