*** 1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        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)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a/1,u/1,v/1,w/1} / {b/1,c/1,d/1}
      Obligation:
        Innermost
        basic terms: {a,u,v,w}/{b,c,d}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      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.
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        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()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        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
        basic terms: {a#,u#,v#,w#}/{b,c,d}
    Applied Processor:
      UsableRules
    Proof:
      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()
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        a#(c(d(x))) -> c_1()
        u#(b(d(d(x)))) -> c_2()
        v#(c(x)) -> c_5()
        w#(c(x)) -> c_8()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      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
        basic terms: {a#,u#,v#,w#}/{b,c,d}
    Applied Processor:
      Trivial
    Proof:
      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.
*** 1.1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      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
        basic terms: {a#,u#,v#,w#}/{b,c,d}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).