*** 1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z)
        e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w)
        e2(x,x,y,z,z,a()) -> e6(x,y,z)
        e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w)
        e2(i(),x,y,z,i(),a()) -> e6(x,y,z)
        e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z)
        e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)
        e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x)
        e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w)
        e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z)
        e5(i(),x,y,z) -> e6(x,y,z)
        f1(x,a()) -> g2(x,x)
        f1(a(),x) -> g1(x,x)
        f2(x,a()) -> g2(x,x)
        f2(a(),x) -> g1(x,x)
        g1(x,a()) -> h2(x)
        g1(a(),x) -> h1(x)
        g2(x,a()) -> h2(x)
        g2(a(),x) -> h1(x)
        h1(a()) -> i()
        h2(a()) -> i()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1} / {a/0,e6/3,i/0}
      Obligation:
        Innermost
        basic terms: {e1,e2,e3,e4,e5,f1,f2,g1,g2,h1,h2}/{a,e6,i}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      We add the following dependency tuples:
      
      Strict DPs
        e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
        e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w))
        e2#(x,x,y,z,z,a()) -> c_3()
        e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w))
        e2#(i(),x,y,z,i(),a()) -> c_5()
        e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6()
        e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
        e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8()
        e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w))
        e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z))
        e5#(i(),x,y,z) -> c_11()
        f1#(x,a()) -> c_12(g2#(x,x))
        f1#(a(),x) -> c_13(g1#(x,x))
        f2#(x,a()) -> c_14(g2#(x,x))
        f2#(a(),x) -> c_15(g1#(x,x))
        g1#(x,a()) -> c_16(h2#(x))
        g1#(a(),x) -> c_17(h1#(x))
        g2#(x,a()) -> c_18(h2#(x))
        g2#(a(),x) -> c_19(h1#(x))
        h1#(a()) -> c_20()
        h2#(a()) -> c_21()
      Weak DPs
        
      
      and mark the set of starting terms.
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
        e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w))
        e2#(x,x,y,z,z,a()) -> c_3()
        e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w))
        e2#(i(),x,y,z,i(),a()) -> c_5()
        e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6()
        e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
        e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8()
        e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w))
        e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z))
        e5#(i(),x,y,z) -> c_11()
        f1#(x,a()) -> c_12(g2#(x,x))
        f1#(a(),x) -> c_13(g1#(x,x))
        f2#(x,a()) -> c_14(g2#(x,x))
        f2#(a(),x) -> c_15(g1#(x,x))
        g1#(x,a()) -> c_16(h2#(x))
        g1#(a(),x) -> c_17(h1#(x))
        g2#(x,a()) -> c_18(h2#(x))
        g2#(a(),x) -> c_19(h1#(x))
        h1#(a()) -> c_20()
        h2#(a()) -> c_21()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z)
        e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w)
        e2(x,x,y,z,z,a()) -> e6(x,y,z)
        e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w)
        e2(i(),x,y,z,i(),a()) -> e6(x,y,z)
        e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z)
        e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)
        e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x)
        e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w)
        e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z)
        e5(i(),x,y,z) -> e6(x,y,z)
        f1(x,a()) -> g2(x,x)
        f1(a(),x) -> g1(x,x)
        f2(x,a()) -> g2(x,x)
        f2(a(),x) -> g1(x,x)
        g1(x,a()) -> h2(x)
        g1(a(),x) -> h1(x)
        g2(x,a()) -> h2(x)
        g2(a(),x) -> h1(x)
        h1(a()) -> i()
        h2(a()) -> i()
      Signature:
        {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0}
      Obligation:
        Innermost
        basic terms: {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1#,h2#}/{a,e6,i}
    Applied Processor:
      UsableRules
    Proof:
      We replace rewrite rules by usable rules:
        e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
        e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w))
        e2#(x,x,y,z,z,a()) -> c_3()
        e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w))
        e2#(i(),x,y,z,i(),a()) -> c_5()
        e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6()
        e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
        e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8()
        e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w))
        e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z))
        e5#(i(),x,y,z) -> c_11()
        f1#(x,a()) -> c_12(g2#(x,x))
        f1#(a(),x) -> c_13(g1#(x,x))
        f2#(x,a()) -> c_14(g2#(x,x))
        f2#(a(),x) -> c_15(g1#(x,x))
        g1#(x,a()) -> c_16(h2#(x))
        g1#(a(),x) -> c_17(h1#(x))
        g2#(x,a()) -> c_18(h2#(x))
        g2#(a(),x) -> c_19(h1#(x))
        h1#(a()) -> c_20()
        h2#(a()) -> c_21()
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
        e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w))
        e2#(x,x,y,z,z,a()) -> c_3()
        e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w))
        e2#(i(),x,y,z,i(),a()) -> c_5()
        e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6()
        e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
        e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8()
        e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w))
        e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z))
        e5#(i(),x,y,z) -> c_11()
        f1#(x,a()) -> c_12(g2#(x,x))
        f1#(a(),x) -> c_13(g1#(x,x))
        f2#(x,a()) -> c_14(g2#(x,x))
        f2#(a(),x) -> c_15(g1#(x,x))
        g1#(x,a()) -> c_16(h2#(x))
        g1#(a(),x) -> c_17(h1#(x))
        g2#(x,a()) -> c_18(h2#(x))
        g2#(a(),x) -> c_19(h1#(x))
        h1#(a()) -> c_20()
        h2#(a()) -> c_21()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0}
      Obligation:
        Innermost
        basic terms: {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1#,h2#}/{a,e6,i}
    Applied Processor:
      Trivial
    Proof:
      Consider the dependency graph
        1:S:e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z))
           -->_1 e5#(i(),x,y,z) -> c_11():11
        
        2:S:e1#(h1(w),h2(w),x,y,z,w) -> c_2(e2#(x,x,y,z,z,w))
           -->_1 e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w)):4
           -->_1 e2#(i(),x,y,z,i(),a()) -> c_5():5
           -->_1 e2#(x,x,y,z,z,a()) -> c_3():3
        
        3:S:e2#(x,x,y,z,z,a()) -> c_3()
           
        
        4:S:e2#(f1(w,w),x,y,z,f2(w,w),w) -> c_4(e3#(x,y,x,y,y,z,y,z,x,y,z,w))
           -->_1 e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)):7
           -->_1 e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6():6
        
        5:S:e2#(i(),x,y,z,i(),a()) -> c_5()
           
        
        6:S:e3#(x,y,x,y,y,z,y,z,x,y,z,a()) -> c_6()
           
        
        7:S:e3#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> c_7(e4#(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w))
           -->_1 e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z)):10
           -->_1 e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8():8
        
        8:S:e4#(x,x,x,x,x,x,x,x,x,x,x,a()) -> c_8()
           
        
        9:S:e4#(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> c_9(e1#(x1,x1,x,y,z,w))
           -->_1 e1#(x1,x1,x,y,z,a()) -> c_1(e5#(x1,x,y,z)):1
        
        10:S:e4#(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> c_10(e5#(x1,x,y,z))
           -->_1 e5#(i(),x,y,z) -> c_11():11
        
        11:S:e5#(i(),x,y,z) -> c_11()
           
        
        12:S:f1#(x,a()) -> c_12(g2#(x,x))
           -->_1 g2#(a(),x) -> c_19(h1#(x)):19
           -->_1 g2#(x,a()) -> c_18(h2#(x)):18
        
        13:S:f1#(a(),x) -> c_13(g1#(x,x))
           -->_1 g1#(a(),x) -> c_17(h1#(x)):17
           -->_1 g1#(x,a()) -> c_16(h2#(x)):16
        
        14:S:f2#(x,a()) -> c_14(g2#(x,x))
           -->_1 g2#(a(),x) -> c_19(h1#(x)):19
           -->_1 g2#(x,a()) -> c_18(h2#(x)):18
        
        15:S:f2#(a(),x) -> c_15(g1#(x,x))
           -->_1 g1#(a(),x) -> c_17(h1#(x)):17
           -->_1 g1#(x,a()) -> c_16(h2#(x)):16
        
        16:S:g1#(x,a()) -> c_16(h2#(x))
           -->_1 h2#(a()) -> c_21():21
        
        17:S:g1#(a(),x) -> c_17(h1#(x))
           -->_1 h1#(a()) -> c_20():20
        
        18:S:g2#(x,a()) -> c_18(h2#(x))
           -->_1 h2#(a()) -> c_21():21
        
        19:S:g2#(a(),x) -> c_19(h1#(x))
           -->_1 h1#(a()) -> c_20():20
        
        20:S:h1#(a()) -> c_20()
           
        
        21:S:h2#(a()) -> c_21()
           
        
      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:
        {e1/6,e2/6,e3/12,e4/12,e5/4,f1/2,f2/2,g1/2,g2/2,h1/1,h2/1,e1#/6,e2#/6,e3#/12,e4#/12,e5#/4,f1#/2,f2#/2,g1#/2,g2#/2,h1#/1,h2#/1} / {a/0,e6/3,i/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/1,c_11/0,c_12/1,c_13/1,c_14/1,c_15/1,c_16/1,c_17/1,c_18/1,c_19/1,c_20/0,c_21/0}
      Obligation:
        Innermost
        basic terms: {e1#,e2#,e3#,e4#,e5#,f1#,f2#,g1#,g2#,h1#,h2#}/{a,e6,i}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).