WORST_CASE(?,O(1))
* Step 1: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            a(c(d(x))) -> c(x)
            u(b(d(d(x)))) -> b(x)
            v(a(a(x))) -> u(v(x))
            v(a(c(x))) -> u(b(d(x)))
            v(c(x)) -> b(x)
            w(a(a(x))) -> u(w(x))
            w(a(c(x))) -> u(b(d(x)))
            w(c(x)) -> b(x)
        - Signature:
            {a/1,u/1,v/1,w/1} / {b/1,c/1,d/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,u,v,w} and constructors {b,c,d}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a#(c(d(x))) -> c_1()
          u#(b(d(d(x)))) -> c_2()
          v#(a(a(x))) -> c_3(u#(v(x)),v#(x))
          v#(a(c(x))) -> c_4(u#(b(d(x))))
          v#(c(x)) -> c_5()
          w#(a(a(x))) -> c_6(u#(w(x)),w#(x))
          w#(a(c(x))) -> c_7(u#(b(d(x))))
          w#(c(x)) -> c_8()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            a#(c(d(x))) -> c_1()
            u#(b(d(d(x)))) -> c_2()
            v#(a(a(x))) -> c_3(u#(v(x)),v#(x))
            v#(a(c(x))) -> c_4(u#(b(d(x))))
            v#(c(x)) -> c_5()
            w#(a(a(x))) -> c_6(u#(w(x)),w#(x))
            w#(a(c(x))) -> c_7(u#(b(d(x))))
            w#(c(x)) -> c_8()
        - Weak TRS:
            a(c(d(x))) -> c(x)
            u(b(d(d(x)))) -> b(x)
            v(a(a(x))) -> u(v(x))
            v(a(c(x))) -> u(b(d(x)))
            v(c(x)) -> b(x)
            w(a(a(x))) -> u(w(x))
            w(a(c(x))) -> u(b(d(x)))
            w(c(x)) -> b(x)
        - Signature:
            {a/1,u/1,v/1,w/1,a#/1,u#/1,v#/1,w#/1} / {b/1,c/1,d/1,c_1/0,c_2/0,c_3/2,c_4/1,c_5/0,c_6/2,c_7/1,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,u#,v#,w#} and constructors {b,c,d}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          a#(c(d(x))) -> c_1()
          u#(b(d(d(x)))) -> c_2()
          v#(c(x)) -> c_5()
          w#(c(x)) -> c_8()
* Step 3: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            a#(c(d(x))) -> c_1()
            u#(b(d(d(x)))) -> c_2()
            v#(c(x)) -> c_5()
            w#(c(x)) -> c_8()
        - Signature:
            {a/1,u/1,v/1,w/1,a#/1,u#/1,v#/1,w#/1} / {b/1,c/1,d/1,c_1/0,c_2/0,c_3/2,c_4/1,c_5/0,c_6/2,c_7/1,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,u#,v#,w#} and constructors {b,c,d}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:a#(c(d(x))) -> c_1()
             
          
          2:S:u#(b(d(d(x)))) -> c_2()
             
          
          3:S:v#(c(x)) -> c_5()
             
          
          4:S:w#(c(x)) -> c_8()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {a/1,u/1,v/1,w/1,a#/1,u#/1,v#/1,w#/1} / {b/1,c/1,d/1,c_1/0,c_2/0,c_3/2,c_4/1,c_5/0,c_6/2,c_7/1,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,u#,v#,w#} and constructors {b,c,d}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))