*** 1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        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)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/3,g/1,h/1,u/3} / {a/0,b/0,c/1,d/0,k/1}
      Obligation:
        Innermost
        basic terms: {f,g,h,u}/{a,b,c,d,k}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      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.
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        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()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        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
        basic terms: {f#,g#,h#,u#}/{a,b,c,d,k}
    Applied Processor:
      UsableRules
    Proof:
      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()
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        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()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        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
        basic terms: {f#,g#,h#,u#}/{a,b,c,d,k}
    Applied Processor:
      Trivial
    Proof:
      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.
*** 1.1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        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
        basic terms: {f#,g#,h#,u#}/{a,b,c,d,k}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).