WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            D'(*(z0,z1)) -> c4(D'(z0))
            D'(*(z0,z1)) -> c5(D'(z1))
            D'(+(z0,z1)) -> c2(D'(z0))
            D'(+(z0,z1)) -> c3(D'(z1))
            D'(-(z0,z1)) -> c6(D'(z0))
            D'(-(z0,z1)) -> c7(D'(z1))
            D'(constant()) -> c1()
            D'(t()) -> c()
        - Weak TRS:
            D(*(z0,z1)) -> +(*(z1,D(z0)),*(z0,D(z1)))
            D(+(z0,z1)) -> +(D(z0),D(z1))
            D(-(z0,z1)) -> -(D(z0),D(z1))
            D(constant()) -> 0()
            D(t()) -> 1()
        - Signature:
            {D/1,D'/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D,D'} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6,c7
            ,constant,t}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            D'(*(z0,z1)) -> c4(D'(z0))
            D'(*(z0,z1)) -> c5(D'(z1))
            D'(+(z0,z1)) -> c2(D'(z0))
            D'(+(z0,z1)) -> c3(D'(z1))
            D'(-(z0,z1)) -> c6(D'(z0))
            D'(-(z0,z1)) -> c7(D'(z1))
            D'(constant()) -> c1()
            D'(t()) -> c()
        - Weak TRS:
            D(*(z0,z1)) -> +(*(z1,D(z0)),*(z0,D(z1)))
            D(+(z0,z1)) -> +(D(z0),D(z1))
            D(-(z0,z1)) -> -(D(z0),D(z1))
            D(constant()) -> 0()
            D(t()) -> 1()
        - Signature:
            {D/1,D'/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D,D'} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6,c7
            ,constant,t}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            D'(*(z0,z1)) -> c4(D'(z0))
            D'(*(z0,z1)) -> c5(D'(z1))
            D'(+(z0,z1)) -> c2(D'(z0))
            D'(+(z0,z1)) -> c3(D'(z1))
            D'(-(z0,z1)) -> c6(D'(z0))
            D'(-(z0,z1)) -> c7(D'(z1))
            D'(constant()) -> c1()
            D'(t()) -> c()
        - Weak TRS:
            D(*(z0,z1)) -> +(*(z1,D(z0)),*(z0,D(z1)))
            D(+(z0,z1)) -> +(D(z0),D(z1))
            D(-(z0,z1)) -> -(D(z0),D(z1))
            D(constant()) -> 0()
            D(t()) -> 1()
        - Signature:
            {D/1,D'/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D,D'} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6,c7
            ,constant,t}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          D'(x){x -> *(x,y)} =
            D'(*(x,y)) ->^+ c4(D'(x))
              = C[D'(x) = D'(x){}]

** Step 1.b:1: DependencyPairs.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            D'(*(z0,z1)) -> c4(D'(z0))
            D'(*(z0,z1)) -> c5(D'(z1))
            D'(+(z0,z1)) -> c2(D'(z0))
            D'(+(z0,z1)) -> c3(D'(z1))
            D'(-(z0,z1)) -> c6(D'(z0))
            D'(-(z0,z1)) -> c7(D'(z1))
            D'(constant()) -> c1()
            D'(t()) -> c()
        - Weak TRS:
            D(*(z0,z1)) -> +(*(z1,D(z0)),*(z0,D(z1)))
            D(+(z0,z1)) -> +(D(z0),D(z1))
            D(-(z0,z1)) -> -(D(z0),D(z1))
            D(constant()) -> 0()
            D(t()) -> 1()
        - Signature:
            {D/1,D'/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D,D'} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6,c7
            ,constant,t}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          D'#(*(z0,z1)) -> c_1(D'#(z0))
          D'#(*(z0,z1)) -> c_2(D'#(z1))
          D'#(+(z0,z1)) -> c_3(D'#(z0))
          D'#(+(z0,z1)) -> c_4(D'#(z1))
          D'#(-(z0,z1)) -> c_5(D'#(z0))
          D'#(-(z0,z1)) -> c_6(D'#(z1))
          D'#(constant()) -> c_7()
          D'#(t()) -> c_8()
        Weak DPs
          D#(*(z0,z1)) -> c_9(D#(z0),D#(z1))
          D#(+(z0,z1)) -> c_10(D#(z0),D#(z1))
          D#(-(z0,z1)) -> c_11(D#(z0),D#(z1))
          D#(constant()) -> c_12()
          D#(t()) -> c_13()
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            D'#(*(z0,z1)) -> c_1(D'#(z0))
            D'#(*(z0,z1)) -> c_2(D'#(z1))
            D'#(+(z0,z1)) -> c_3(D'#(z0))
            D'#(+(z0,z1)) -> c_4(D'#(z1))
            D'#(-(z0,z1)) -> c_5(D'#(z0))
            D'#(-(z0,z1)) -> c_6(D'#(z1))
            D'#(constant()) -> c_7()
            D'#(t()) -> c_8()
        - Weak DPs:
            D#(*(z0,z1)) -> c_9(D#(z0),D#(z1))
            D#(+(z0,z1)) -> c_10(D#(z0),D#(z1))
            D#(-(z0,z1)) -> c_11(D#(z0),D#(z1))
            D#(constant()) -> c_12()
            D#(t()) -> c_13()
        - Weak TRS:
            D(*(z0,z1)) -> +(*(z1,D(z0)),*(z0,D(z1)))
            D(+(z0,z1)) -> +(D(z0),D(z1))
            D(-(z0,z1)) -> -(D(z0),D(z1))
            D(constant()) -> 0()
            D(t()) -> 1()
            D'(*(z0,z1)) -> c4(D'(z0))
            D'(*(z0,z1)) -> c5(D'(z1))
            D'(+(z0,z1)) -> c2(D'(z0))
            D'(+(z0,z1)) -> c3(D'(z1))
            D'(-(z0,z1)) -> c6(D'(z0))
            D'(-(z0,z1)) -> c7(D'(z1))
            D'(constant()) -> c1()
            D'(t()) -> c()
        - Signature:
            {D/1,D'/1,D#/1,D'#/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0,c_1/1
            ,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D#,D'#} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6
            ,c7,constant,t}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {7,8}
        by application of
          Pre({7,8}) = {1,2,3,4,5,6}.
        Here rules are labelled as follows:
          1: D'#(*(z0,z1)) -> c_1(D'#(z0))
          2: D'#(*(z0,z1)) -> c_2(D'#(z1))
          3: D'#(+(z0,z1)) -> c_3(D'#(z0))
          4: D'#(+(z0,z1)) -> c_4(D'#(z1))
          5: D'#(-(z0,z1)) -> c_5(D'#(z0))
          6: D'#(-(z0,z1)) -> c_6(D'#(z1))
          7: D'#(constant()) -> c_7()
          8: D'#(t()) -> c_8()
          9: D#(*(z0,z1)) -> c_9(D#(z0),D#(z1))
          10: D#(+(z0,z1)) -> c_10(D#(z0),D#(z1))
          11: D#(-(z0,z1)) -> c_11(D#(z0),D#(z1))
          12: D#(constant()) -> c_12()
          13: D#(t()) -> c_13()
** Step 1.b:3: RemoveWeakSuffixes.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            D'#(*(z0,z1)) -> c_1(D'#(z0))
            D'#(*(z0,z1)) -> c_2(D'#(z1))
            D'#(+(z0,z1)) -> c_3(D'#(z0))
            D'#(+(z0,z1)) -> c_4(D'#(z1))
            D'#(-(z0,z1)) -> c_5(D'#(z0))
            D'#(-(z0,z1)) -> c_6(D'#(z1))
        - Weak DPs:
            D#(*(z0,z1)) -> c_9(D#(z0),D#(z1))
            D#(+(z0,z1)) -> c_10(D#(z0),D#(z1))
            D#(-(z0,z1)) -> c_11(D#(z0),D#(z1))
            D#(constant()) -> c_12()
            D#(t()) -> c_13()
            D'#(constant()) -> c_7()
            D'#(t()) -> c_8()
        - Weak TRS:
            D(*(z0,z1)) -> +(*(z1,D(z0)),*(z0,D(z1)))
            D(+(z0,z1)) -> +(D(z0),D(z1))
            D(-(z0,z1)) -> -(D(z0),D(z1))
            D(constant()) -> 0()
            D(t()) -> 1()
            D'(*(z0,z1)) -> c4(D'(z0))
            D'(*(z0,z1)) -> c5(D'(z1))
            D'(+(z0,z1)) -> c2(D'(z0))
            D'(+(z0,z1)) -> c3(D'(z1))
            D'(-(z0,z1)) -> c6(D'(z0))
            D'(-(z0,z1)) -> c7(D'(z1))
            D'(constant()) -> c1()
            D'(t()) -> c()
        - Signature:
            {D/1,D'/1,D#/1,D'#/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0,c_1/1
            ,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D#,D'#} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6
            ,c7,constant,t}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:D'#(*(z0,z1)) -> c_1(D'#(z0))
             -->_1 D'#(-(z0,z1)) -> c_6(D'#(z1)):6
             -->_1 D'#(-(z0,z1)) -> c_5(D'#(z0)):5
             -->_1 D'#(+(z0,z1)) -> c_4(D'#(z1)):4
             -->_1 D'#(+(z0,z1)) -> c_3(D'#(z0)):3
             -->_1 D'#(*(z0,z1)) -> c_2(D'#(z1)):2
             -->_1 D'#(t()) -> c_8():13
             -->_1 D'#(constant()) -> c_7():12
             -->_1 D'#(*(z0,z1)) -> c_1(D'#(z0)):1
          
          2:S:D'#(*(z0,z1)) -> c_2(D'#(z1))
             -->_1 D'#(-(z0,z1)) -> c_6(D'#(z1)):6
             -->_1 D'#(-(z0,z1)) -> c_5(D'#(z0)):5
             -->_1 D'#(+(z0,z1)) -> c_4(D'#(z1)):4
             -->_1 D'#(+(z0,z1)) -> c_3(D'#(z0)):3
             -->_1 D'#(t()) -> c_8():13
             -->_1 D'#(constant()) -> c_7():12
             -->_1 D'#(*(z0,z1)) -> c_2(D'#(z1)):2
             -->_1 D'#(*(z0,z1)) -> c_1(D'#(z0)):1
          
          3:S:D'#(+(z0,z1)) -> c_3(D'#(z0))
             -->_1 D'#(-(z0,z1)) -> c_6(D'#(z1)):6
             -->_1 D'#(-(z0,z1)) -> c_5(D'#(z0)):5
             -->_1 D'#(+(z0,z1)) -> c_4(D'#(z1)):4
             -->_1 D'#(t()) -> c_8():13
             -->_1 D'#(constant()) -> c_7():12
             -->_1 D'#(+(z0,z1)) -> c_3(D'#(z0)):3
             -->_1 D'#(*(z0,z1)) -> c_2(D'#(z1)):2
             -->_1 D'#(*(z0,z1)) -> c_1(D'#(z0)):1
          
          4:S:D'#(+(z0,z1)) -> c_4(D'#(z1))
             -->_1 D'#(-(z0,z1)) -> c_6(D'#(z1)):6
             -->_1 D'#(-(z0,z1)) -> c_5(D'#(z0)):5
             -->_1 D'#(t()) -> c_8():13
             -->_1 D'#(constant()) -> c_7():12
             -->_1 D'#(+(z0,z1)) -> c_4(D'#(z1)):4
             -->_1 D'#(+(z0,z1)) -> c_3(D'#(z0)):3
             -->_1 D'#(*(z0,z1)) -> c_2(D'#(z1)):2
             -->_1 D'#(*(z0,z1)) -> c_1(D'#(z0)):1
          
          5:S:D'#(-(z0,z1)) -> c_5(D'#(z0))
             -->_1 D'#(-(z0,z1)) -> c_6(D'#(z1)):6
             -->_1 D'#(t()) -> c_8():13
             -->_1 D'#(constant()) -> c_7():12
             -->_1 D'#(-(z0,z1)) -> c_5(D'#(z0)):5
             -->_1 D'#(+(z0,z1)) -> c_4(D'#(z1)):4
             -->_1 D'#(+(z0,z1)) -> c_3(D'#(z0)):3
             -->_1 D'#(*(z0,z1)) -> c_2(D'#(z1)):2
             -->_1 D'#(*(z0,z1)) -> c_1(D'#(z0)):1
          
          6:S:D'#(-(z0,z1)) -> c_6(D'#(z1))
             -->_1 D'#(t()) -> c_8():13
             -->_1 D'#(constant()) -> c_7():12
             -->_1 D'#(-(z0,z1)) -> c_6(D'#(z1)):6
             -->_1 D'#(-(z0,z1)) -> c_5(D'#(z0)):5
             -->_1 D'#(+(z0,z1)) -> c_4(D'#(z1)):4
             -->_1 D'#(+(z0,z1)) -> c_3(D'#(z0)):3
             -->_1 D'#(*(z0,z1)) -> c_2(D'#(z1)):2
             -->_1 D'#(*(z0,z1)) -> c_1(D'#(z0)):1
          
          7:W:D#(*(z0,z1)) -> c_9(D#(z0),D#(z1))
             -->_2 D#(-(z0,z1)) -> c_11(D#(z0),D#(z1)):9
             -->_1 D#(-(z0,z1)) -> c_11(D#(z0),D#(z1)):9
             -->_2 D#(+(z0,z1)) -> c_10(D#(z0),D#(z1)):8
             -->_1 D#(+(z0,z1)) -> c_10(D#(z0),D#(z1)):8
             -->_2 D#(t()) -> c_13():11
             -->_1 D#(t()) -> c_13():11
             -->_2 D#(constant()) -> c_12():10
             -->_1 D#(constant()) -> c_12():10
             -->_2 D#(*(z0,z1)) -> c_9(D#(z0),D#(z1)):7
             -->_1 D#(*(z0,z1)) -> c_9(D#(z0),D#(z1)):7
          
          8:W:D#(+(z0,z1)) -> c_10(D#(z0),D#(z1))
             -->_2 D#(-(z0,z1)) -> c_11(D#(z0),D#(z1)):9
             -->_1 D#(-(z0,z1)) -> c_11(D#(z0),D#(z1)):9
             -->_2 D#(t()) -> c_13():11
             -->_1 D#(t()) -> c_13():11
             -->_2 D#(constant()) -> c_12():10
             -->_1 D#(constant()) -> c_12():10
             -->_2 D#(+(z0,z1)) -> c_10(D#(z0),D#(z1)):8
             -->_1 D#(+(z0,z1)) -> c_10(D#(z0),D#(z1)):8
             -->_2 D#(*(z0,z1)) -> c_9(D#(z0),D#(z1)):7
             -->_1 D#(*(z0,z1)) -> c_9(D#(z0),D#(z1)):7
          
          9:W:D#(-(z0,z1)) -> c_11(D#(z0),D#(z1))
             -->_2 D#(t()) -> c_13():11
             -->_1 D#(t()) -> c_13():11
             -->_2 D#(constant()) -> c_12():10
             -->_1 D#(constant()) -> c_12():10
             -->_2 D#(-(z0,z1)) -> c_11(D#(z0),D#(z1)):9
             -->_1 D#(-(z0,z1)) -> c_11(D#(z0),D#(z1)):9
             -->_2 D#(+(z0,z1)) -> c_10(D#(z0),D#(z1)):8
             -->_1 D#(+(z0,z1)) -> c_10(D#(z0),D#(z1)):8
             -->_2 D#(*(z0,z1)) -> c_9(D#(z0),D#(z1)):7
             -->_1 D#(*(z0,z1)) -> c_9(D#(z0),D#(z1)):7
          
          10:W:D#(constant()) -> c_12()
             
          
          11:W:D#(t()) -> c_13()
             
          
          12:W:D'#(constant()) -> c_7()
             
          
          13:W:D'#(t()) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          7: D#(*(z0,z1)) -> c_9(D#(z0),D#(z1))
          9: D#(-(z0,z1)) -> c_11(D#(z0),D#(z1))
          8: D#(+(z0,z1)) -> c_10(D#(z0),D#(z1))
          10: D#(constant()) -> c_12()
          11: D#(t()) -> c_13()
          12: D'#(constant()) -> c_7()
          13: D'#(t()) -> c_8()
** Step 1.b:4: UsableRules.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            D'#(*(z0,z1)) -> c_1(D'#(z0))
            D'#(*(z0,z1)) -> c_2(D'#(z1))
            D'#(+(z0,z1)) -> c_3(D'#(z0))
            D'#(+(z0,z1)) -> c_4(D'#(z1))
            D'#(-(z0,z1)) -> c_5(D'#(z0))
            D'#(-(z0,z1)) -> c_6(D'#(z1))
        - Weak TRS:
            D(*(z0,z1)) -> +(*(z1,D(z0)),*(z0,D(z1)))
            D(+(z0,z1)) -> +(D(z0),D(z1))
            D(-(z0,z1)) -> -(D(z0),D(z1))
            D(constant()) -> 0()
            D(t()) -> 1()
            D'(*(z0,z1)) -> c4(D'(z0))
            D'(*(z0,z1)) -> c5(D'(z1))
            D'(+(z0,z1)) -> c2(D'(z0))
            D'(+(z0,z1)) -> c3(D'(z1))
            D'(-(z0,z1)) -> c6(D'(z0))
            D'(-(z0,z1)) -> c7(D'(z1))
            D'(constant()) -> c1()
            D'(t()) -> c()
        - Signature:
            {D/1,D'/1,D#/1,D'#/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0,c_1/1
            ,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D#,D'#} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6
            ,c7,constant,t}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          D'#(*(z0,z1)) -> c_1(D'#(z0))
          D'#(*(z0,z1)) -> c_2(D'#(z1))
          D'#(+(z0,z1)) -> c_3(D'#(z0))
          D'#(+(z0,z1)) -> c_4(D'#(z1))
          D'#(-(z0,z1)) -> c_5(D'#(z0))
          D'#(-(z0,z1)) -> c_6(D'#(z1))
** Step 1.b:5: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            D'#(*(z0,z1)) -> c_1(D'#(z0))
            D'#(*(z0,z1)) -> c_2(D'#(z1))
            D'#(+(z0,z1)) -> c_3(D'#(z0))
            D'#(+(z0,z1)) -> c_4(D'#(z1))
            D'#(-(z0,z1)) -> c_5(D'#(z0))
            D'#(-(z0,z1)) -> c_6(D'#(z1))
        - Signature:
            {D/1,D'/1,D#/1,D'#/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0,c_1/1
            ,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D#,D'#} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6
            ,c7,constant,t}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_2) = {1},
          uargs(c_3) = {1},
          uargs(c_4) = {1},
          uargs(c_5) = {1},
          uargs(c_6) = {1}
        
        Following symbols are considered usable:
          {D#,D'#}
        TcT has computed the following interpretation:
                 p(*) = [1] x1 + [1] x2 + [0]
                 p(+) = [1] x1 + [1] x2 + [1]
                 p(-) = [1] x1 + [1] x2 + [0]
                 p(0) = [2]                  
                 p(1) = [2]                  
                 p(D) = [4]                  
                p(D') = [4]                  
                 p(c) = [0]                  
                p(c1) = [2]                  
                p(c2) = [1]                  
                p(c3) = [4]                  
                p(c4) = [1]                  
                p(c5) = [2]                  
                p(c6) = [0]                  
                p(c7) = [1] x1 + [1]         
          p(constant) = [0]                  
                 p(t) = [2]                  
                p(D#) = [2]                  
               p(D'#) = [4] x1 + [0]         
               p(c_1) = [1] x1 + [0]         
               p(c_2) = [1] x1 + [0]         
               p(c_3) = [1] x1 + [1]         
               p(c_4) = [1] x1 + [4]         
               p(c_5) = [1] x1 + [0]         
               p(c_6) = [1] x1 + [0]         
               p(c_7) = [1]                  
               p(c_8) = [0]                  
               p(c_9) = [2] x1 + [1]         
              p(c_10) = [1]                  
              p(c_11) = [2] x1 + [1] x2 + [2]
              p(c_12) = [0]                  
              p(c_13) = [1]                  
        
        Following rules are strictly oriented:
        D'#(+(z0,z1)) = [4] z0 + [4] z1 + [4]
                      > [4] z0 + [1]         
                      = c_3(D'#(z0))         
        
        
        Following rules are (at-least) weakly oriented:
        D'#(*(z0,z1)) =  [4] z0 + [4] z1 + [0]
                      >= [4] z0 + [0]         
                      =  c_1(D'#(z0))         
        
        D'#(*(z0,z1)) =  [4] z0 + [4] z1 + [0]
                      >= [4] z1 + [0]         
                      =  c_2(D'#(z1))         
        
        D'#(+(z0,z1)) =  [4] z0 + [4] z1 + [4]
                      >= [4] z1 + [4]         
                      =  c_4(D'#(z1))         
        
        D'#(-(z0,z1)) =  [4] z0 + [4] z1 + [0]
                      >= [4] z0 + [0]         
                      =  c_5(D'#(z0))         
        
        D'#(-(z0,z1)) =  [4] z0 + [4] z1 + [0]
                      >= [4] z1 + [0]         
                      =  c_6(D'#(z1))         
        
** Step 1.b:6: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            D'#(*(z0,z1)) -> c_1(D'#(z0))
            D'#(*(z0,z1)) -> c_2(D'#(z1))
            D'#(+(z0,z1)) -> c_4(D'#(z1))
            D'#(-(z0,z1)) -> c_5(D'#(z0))
            D'#(-(z0,z1)) -> c_6(D'#(z1))
        - Weak DPs:
            D'#(+(z0,z1)) -> c_3(D'#(z0))
        - Signature:
            {D/1,D'/1,D#/1,D'#/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0,c_1/1
            ,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D#,D'#} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6
            ,c7,constant,t}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_2) = {1},
          uargs(c_3) = {1},
          uargs(c_4) = {1},
          uargs(c_5) = {1},
          uargs(c_6) = {1}
        
        Following symbols are considered usable:
          {D#,D'#}
        TcT has computed the following interpretation:
                 p(*) = [1] x1 + [1] x2 + [0]
                 p(+) = [1] x1 + [1] x2 + [4]
                 p(-) = [1] x1 + [1] x2 + [0]
                 p(0) = [2]                  
                 p(1) = [0]                  
                 p(D) = [1] x1 + [1]         
                p(D') = [1]                  
                 p(c) = [0]                  
                p(c1) = [4]                  
                p(c2) = [1] x1 + [1]         
                p(c3) = [1] x1 + [0]         
                p(c4) = [1] x1 + [0]         
                p(c5) = [1] x1 + [1]         
                p(c6) = [1]                  
                p(c7) = [1] x1 + [4]         
          p(constant) = [4]                  
                 p(t) = [0]                  
                p(D#) = [1]                  
               p(D'#) = [2] x1 + [0]         
               p(c_1) = [1] x1 + [0]         
               p(c_2) = [1] x1 + [0]         
               p(c_3) = [1] x1 + [8]         
               p(c_4) = [1] x1 + [4]         
               p(c_5) = [1] x1 + [0]         
               p(c_6) = [1] x1 + [0]         
               p(c_7) = [1]                  
               p(c_8) = [1]                  
               p(c_9) = [1] x1 + [2] x2 + [0]
              p(c_10) = [1] x2 + [8]         
              p(c_11) = [1] x1 + [1]         
              p(c_12) = [2]                  
              p(c_13) = [0]                  
        
        Following rules are strictly oriented:
        D'#(+(z0,z1)) = [2] z0 + [2] z1 + [8]
                      > [2] z1 + [4]         
                      = c_4(D'#(z1))         
        
        
        Following rules are (at-least) weakly oriented:
        D'#(*(z0,z1)) =  [2] z0 + [2] z1 + [0]
                      >= [2] z0 + [0]         
                      =  c_1(D'#(z0))         
        
        D'#(*(z0,z1)) =  [2] z0 + [2] z1 + [0]
                      >= [2] z1 + [0]         
                      =  c_2(D'#(z1))         
        
        D'#(+(z0,z1)) =  [2] z0 + [2] z1 + [8]
                      >= [2] z0 + [8]         
                      =  c_3(D'#(z0))         
        
        D'#(-(z0,z1)) =  [2] z0 + [2] z1 + [0]
                      >= [2] z0 + [0]         
                      =  c_5(D'#(z0))         
        
        D'#(-(z0,z1)) =  [2] z0 + [2] z1 + [0]
                      >= [2] z1 + [0]         
                      =  c_6(D'#(z1))         
        
** Step 1.b:7: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            D'#(*(z0,z1)) -> c_1(D'#(z0))
            D'#(*(z0,z1)) -> c_2(D'#(z1))
            D'#(-(z0,z1)) -> c_5(D'#(z0))
            D'#(-(z0,z1)) -> c_6(D'#(z1))
        - Weak DPs:
            D'#(+(z0,z1)) -> c_3(D'#(z0))
            D'#(+(z0,z1)) -> c_4(D'#(z1))
        - Signature:
            {D/1,D'/1,D#/1,D'#/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0,c_1/1
            ,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D#,D'#} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6
            ,c7,constant,t}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_2) = {1},
          uargs(c_3) = {1},
          uargs(c_4) = {1},
          uargs(c_5) = {1},
          uargs(c_6) = {1}
        
        Following symbols are considered usable:
          {D#,D'#}
        TcT has computed the following interpretation:
                 p(*) = [1] x1 + [1] x2 + [4] 
                 p(+) = [1] x1 + [1] x2 + [12]
                 p(-) = [1] x1 + [1] x2 + [0] 
                 p(0) = [2]                   
                 p(1) = [1]                   
                 p(D) = [1]                   
                p(D') = [1]                   
                 p(c) = [2]                   
                p(c1) = [1]                   
                p(c2) = [1]                   
                p(c3) = [0]                   
                p(c4) = [1] x1 + [1]          
                p(c5) = [1]                   
                p(c6) = [0]                   
                p(c7) = [1] x1 + [1]          
          p(constant) = [0]                   
                 p(t) = [1]                   
                p(D#) = [1]                   
               p(D'#) = [1] x1 + [0]          
               p(c_1) = [1] x1 + [0]          
               p(c_2) = [1] x1 + [4]          
               p(c_3) = [1] x1 + [12]         
               p(c_4) = [1] x1 + [12]         
               p(c_5) = [1] x1 + [0]          
               p(c_6) = [1] x1 + [0]          
               p(c_7) = [8]                   
               p(c_8) = [8]                   
               p(c_9) = [1] x1 + [8]          
              p(c_10) = [8] x1 + [1] x2 + [4] 
              p(c_11) = [1]                   
              p(c_12) = [0]                   
              p(c_13) = [1]                   
        
        Following rules are strictly oriented:
        D'#(*(z0,z1)) = [1] z0 + [1] z1 + [4]
                      > [1] z0 + [0]         
                      = c_1(D'#(z0))         
        
        
        Following rules are (at-least) weakly oriented:
        D'#(*(z0,z1)) =  [1] z0 + [1] z1 + [4] 
                      >= [1] z1 + [4]          
                      =  c_2(D'#(z1))          
        
        D'#(+(z0,z1)) =  [1] z0 + [1] z1 + [12]
                      >= [1] z0 + [12]         
                      =  c_3(D'#(z0))          
        
        D'#(+(z0,z1)) =  [1] z0 + [1] z1 + [12]
                      >= [1] z1 + [12]         
                      =  c_4(D'#(z1))          
        
        D'#(-(z0,z1)) =  [1] z0 + [1] z1 + [0] 
                      >= [1] z0 + [0]          
                      =  c_5(D'#(z0))          
        
        D'#(-(z0,z1)) =  [1] z0 + [1] z1 + [0] 
                      >= [1] z1 + [0]          
                      =  c_6(D'#(z1))          
        
** Step 1.b:8: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            D'#(*(z0,z1)) -> c_2(D'#(z1))
            D'#(-(z0,z1)) -> c_5(D'#(z0))
            D'#(-(z0,z1)) -> c_6(D'#(z1))
        - Weak DPs:
            D'#(*(z0,z1)) -> c_1(D'#(z0))
            D'#(+(z0,z1)) -> c_3(D'#(z0))
            D'#(+(z0,z1)) -> c_4(D'#(z1))
        - Signature:
            {D/1,D'/1,D#/1,D'#/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0,c_1/1
            ,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D#,D'#} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6
            ,c7,constant,t}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_2) = {1},
          uargs(c_3) = {1},
          uargs(c_4) = {1},
          uargs(c_5) = {1},
          uargs(c_6) = {1}
        
        Following symbols are considered usable:
          {D#,D'#}
        TcT has computed the following interpretation:
                 p(*) = [1] x1 + [1] x2 + [10]
                 p(+) = [1] x1 + [1] x2 + [0] 
                 p(-) = [1] x1 + [1] x2 + [6] 
                 p(0) = [1]                   
                 p(1) = [0]                   
                 p(D) = [1]                   
                p(D') = [1] x1 + [0]          
                 p(c) = [0]                   
                p(c1) = [8]                   
                p(c2) = [1] x1 + [0]          
                p(c3) = [2]                   
                p(c4) = [1] x1 + [1]          
                p(c5) = [2]                   
                p(c6) = [1]                   
                p(c7) = [0]                   
          p(constant) = [0]                   
                 p(t) = [2]                   
                p(D#) = [0]                   
               p(D'#) = [2] x1 + [0]          
               p(c_1) = [1] x1 + [1]          
               p(c_2) = [1] x1 + [15]         
               p(c_3) = [1] x1 + [0]          
               p(c_4) = [1] x1 + [0]          
               p(c_5) = [1] x1 + [2]          
               p(c_6) = [1] x1 + [12]         
               p(c_7) = [0]                   
               p(c_8) = [1]                   
               p(c_9) = [2]                   
              p(c_10) = [1] x1 + [2] x2 + [4] 
              p(c_11) = [2]                   
              p(c_12) = [0]                   
              p(c_13) = [1]                   
        
        Following rules are strictly oriented:
        D'#(*(z0,z1)) = [2] z0 + [2] z1 + [20]
                      > [2] z1 + [15]         
                      = c_2(D'#(z1))          
        
        D'#(-(z0,z1)) = [2] z0 + [2] z1 + [12]
                      > [2] z0 + [2]          
                      = c_5(D'#(z0))          
        
        
        Following rules are (at-least) weakly oriented:
        D'#(*(z0,z1)) =  [2] z0 + [2] z1 + [20]
                      >= [2] z0 + [1]          
                      =  c_1(D'#(z0))          
        
        D'#(+(z0,z1)) =  [2] z0 + [2] z1 + [0] 
                      >= [2] z0 + [0]          
                      =  c_3(D'#(z0))          
        
        D'#(+(z0,z1)) =  [2] z0 + [2] z1 + [0] 
                      >= [2] z1 + [0]          
                      =  c_4(D'#(z1))          
        
        D'#(-(z0,z1)) =  [2] z0 + [2] z1 + [12]
                      >= [2] z1 + [12]         
                      =  c_6(D'#(z1))          
        
** Step 1.b:9: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            D'#(-(z0,z1)) -> c_6(D'#(z1))
        - Weak DPs:
            D'#(*(z0,z1)) -> c_1(D'#(z0))
            D'#(*(z0,z1)) -> c_2(D'#(z1))
            D'#(+(z0,z1)) -> c_3(D'#(z0))
            D'#(+(z0,z1)) -> c_4(D'#(z1))
            D'#(-(z0,z1)) -> c_5(D'#(z0))
        - Signature:
            {D/1,D'/1,D#/1,D'#/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0,c_1/1
            ,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D#,D'#} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6
            ,c7,constant,t}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_2) = {1},
          uargs(c_3) = {1},
          uargs(c_4) = {1},
          uargs(c_5) = {1},
          uargs(c_6) = {1}
        
        Following symbols are considered usable:
          {D#,D'#}
        TcT has computed the following interpretation:
                 p(*) = [1] x1 + [1] x2 + [1]
                 p(+) = [1] x1 + [1] x2 + [0]
                 p(-) = [1] x1 + [1] x2 + [4]
                 p(0) = [1]                  
                 p(1) = [0]                  
                 p(D) = [1] x1 + [1]         
                p(D') = [2] x1 + [1]         
                 p(c) = [4]                  
                p(c1) = [8]                  
                p(c2) = [1]                  
                p(c3) = [2]                  
                p(c4) = [1] x1 + [1]         
                p(c5) = [1] x1 + [2]         
                p(c6) = [1] x1 + [2]         
                p(c7) = [1] x1 + [1]         
          p(constant) = [0]                  
                 p(t) = [1]                  
                p(D#) = [1] x1 + [1]         
               p(D'#) = [4] x1 + [0]         
               p(c_1) = [1] x1 + [3]         
               p(c_2) = [1] x1 + [0]         
               p(c_3) = [1] x1 + [0]         
               p(c_4) = [1] x1 + [0]         
               p(c_5) = [1] x1 + [2]         
               p(c_6) = [1] x1 + [8]         
               p(c_7) = [2]                  
               p(c_8) = [1]                  
               p(c_9) = [1] x1 + [1]         
              p(c_10) = [1] x2 + [0]         
              p(c_11) = [1] x1 + [1] x2 + [1]
              p(c_12) = [1]                  
              p(c_13) = [1]                  
        
        Following rules are strictly oriented:
        D'#(-(z0,z1)) = [4] z0 + [4] z1 + [16]
                      > [4] z1 + [8]          
                      = c_6(D'#(z1))          
        
        
        Following rules are (at-least) weakly oriented:
        D'#(*(z0,z1)) =  [4] z0 + [4] z1 + [4] 
                      >= [4] z0 + [3]          
                      =  c_1(D'#(z0))          
        
        D'#(*(z0,z1)) =  [4] z0 + [4] z1 + [4] 
                      >= [4] z1 + [0]          
                      =  c_2(D'#(z1))          
        
        D'#(+(z0,z1)) =  [4] z0 + [4] z1 + [0] 
                      >= [4] z0 + [0]          
                      =  c_3(D'#(z0))          
        
        D'#(+(z0,z1)) =  [4] z0 + [4] z1 + [0] 
                      >= [4] z1 + [0]          
                      =  c_4(D'#(z1))          
        
        D'#(-(z0,z1)) =  [4] z0 + [4] z1 + [16]
                      >= [4] z0 + [2]          
                      =  c_5(D'#(z0))          
        
** Step 1.b:10: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            D'#(*(z0,z1)) -> c_1(D'#(z0))
            D'#(*(z0,z1)) -> c_2(D'#(z1))
            D'#(+(z0,z1)) -> c_3(D'#(z0))
            D'#(+(z0,z1)) -> c_4(D'#(z1))
            D'#(-(z0,z1)) -> c_5(D'#(z0))
            D'#(-(z0,z1)) -> c_6(D'#(z1))
        - Signature:
            {D/1,D'/1,D#/1,D'#/1} / {*/2,+/2,-/2,0/0,1/0,c/0,c1/0,c2/1,c3/1,c4/1,c5/1,c6/1,c7/1,constant/0,t/0,c_1/1
            ,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {D#,D'#} and constructors {*,+,-,0,1,c,c1,c2,c3,c4,c5,c6
            ,c7,constant,t}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))