MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1} / {or/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,not} and constructors {or}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
          and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
          not#(and(x,y)) -> c_3(not#(x),not#(y))
          not#(not(x)) -> c_4()
          not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
            and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(not(x)) -> c_4()
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {4}
        by application of
          Pre({4}) = {3,5}.
        Here rules are labelled as follows:
          1: and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
          2: and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
          3: not#(and(x,y)) -> c_3(not#(x),not#(y))
          4: not#(not(x)) -> c_4()
          5: not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
            and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak DPs:
            not#(not(x)) -> c_4()
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
             -->_2 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):2
             -->_1 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):2
             -->_2 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):1
             -->_1 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):1
          
          2:S:and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
             -->_2 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):2
             -->_1 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):2
             -->_2 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):1
             -->_1 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):1
          
          3:S:not#(and(x,y)) -> c_3(not#(x),not#(y))
             -->_2 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):4
             -->_1 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):4
             -->_2 not#(not(x)) -> c_4():5
             -->_1 not#(not(x)) -> c_4():5
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):3
             -->_1 not#(and(x,y)) -> c_3(not#(x),not#(y)):3
          
          4:S:not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
             -->_3 not#(not(x)) -> c_4():5
             -->_2 not#(not(x)) -> c_4():5
             -->_3 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):4
             -->_2 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):4
             -->_3 not#(and(x,y)) -> c_3(not#(x),not#(y)):3
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):3
             -->_1 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):2
             -->_1 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):1
          
          5:W:not#(not(x)) -> c_4()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          5: not#(not(x)) -> c_4()
* Step 4: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
            and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
              and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
          - Weak DPs:
              not#(and(x,y)) -> c_3(not#(x),not#(y))
              not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
          - Weak TRS:
              and(x,or(y,z)) -> or(and(x,y),and(x,z))
              and(or(y,z),x) -> or(and(x,y),and(x,z))
              not(and(x,y)) -> or(not(x),not(y))
              not(not(x)) -> x
              not(or(x,y)) -> and(not(x),not(y))
          - Signature:
              {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
        
        Problem (S)
          - Strict DPs:
              not#(and(x,y)) -> c_3(not#(x),not#(y))
              not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
          - Weak DPs:
              and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
              and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
          - Weak TRS:
              and(x,or(y,z)) -> or(and(x,y),and(x,z))
              and(or(y,z),x) -> or(and(x,y),and(x,z))
              not(and(x,y)) -> or(not(x),not(y))
              not(not(x)) -> x
              not(or(x,y)) -> and(not(x),not(y))
          - Signature:
              {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
** Step 4.a:1: DecomposeDG MAYBE
    + Considered Problem:
        - Strict DPs:
            and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
            and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Just someStrategy, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          not#(and(x,y)) -> c_3(not#(x),not#(y))
          not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        and a lower component
          and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
          and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
        Further, following extension rules are added to the lower component.
          not#(and(x,y)) -> not#(x)
          not#(and(x,y)) -> not#(y)
          not#(or(x,y)) -> and#(not(x),not(y))
          not#(or(x,y)) -> not#(x)
          not#(or(x,y)) -> not#(y)
*** Step 4.a:1.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
          
        The strictly oriented rules are moved into the weak component.
**** Step 4.a:1.a:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_3) = {1,2},
          uargs(c_5) = {1,2,3}
        
        Following symbols are considered usable:
          {and#,not#}
        TcT has computed the following interpretation:
           p(and) = [2] x1 + [2] x2 + [12]        
           p(not) = [4]                           
            p(or) = [1] x1 + [1] x2 + [5]         
          p(and#) = [0]                           
          p(not#) = [2] x1 + [1]                  
           p(c_1) = [2] x1 + [4] x2 + [0]         
           p(c_2) = [2] x1 + [0]                  
           p(c_3) = [1] x1 + [2] x2 + [6]         
           p(c_4) = [1]                           
           p(c_5) = [1] x1 + [1] x2 + [1] x3 + [8]
        
        Following rules are strictly oriented:
        not#(or(x,y)) = [2] x + [2] y + [11]                    
                      > [2] x + [2] y + [10]                    
                      = c_5(and#(not(x),not(y)),not#(x),not#(y))
        
        
        Following rules are (at-least) weakly oriented:
        not#(and(x,y)) =  [4] x + [4] y + [25]
                       >= [2] x + [4] y + [9] 
                       =  c_3(not#(x),not#(y))
        
**** Step 4.a:1.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 4.a:1.a:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:not#(and(x,y)) -> c_3(not#(x),not#(y))
             -->_2 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_1 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
             -->_1 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
          
          2:W:not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
             -->_3 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_2 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_3 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: not#(and(x,y)) -> c_3(not#(x),not#(y))
          2: not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
**** Step 4.a:1.a:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 4.a:1.b:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
          and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
      - Weak DPs:
          not#(and(x,y)) -> not#(x)
          not#(and(x,y)) -> not#(y)
          not#(or(x,y)) -> and#(not(x),not(y))
          not#(or(x,y)) -> not#(x)
          not#(or(x,y)) -> not#(y)
      - Weak TRS:
          and(x,or(y,z)) -> or(and(x,y),and(x,z))
          and(or(y,z),x) -> or(and(x,y),and(x,z))
          not(and(x,y)) -> or(not(x),not(y))
          not(not(x)) -> x
          not(or(x,y)) -> and(not(x),not(y))
      - Signature:
          {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 4.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak DPs:
            and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
            and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:not#(and(x,y)) -> c_3(not#(x),not#(y))
             -->_2 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_1 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
             -->_1 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
          
          2:S:not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
             -->_1 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):4
             -->_1 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):3
             -->_3 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_2 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_3 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
          
          3:W:and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
             -->_2 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):4
             -->_1 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):4
             -->_2 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):3
             -->_1 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):3
          
          4:W:and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
             -->_2 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):4
             -->_1 and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z)):4
             -->_2 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):3
             -->_1 and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z)):3
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: and#(or(y,z),x) -> c_2(and#(x,y),and#(x,z))
          3: and#(x,or(y,z)) -> c_1(and#(x,y),and#(x,z))
** Step 4.b:2: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:not#(and(x,y)) -> c_3(not#(x),not#(y))
             -->_2 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_1 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
             -->_1 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
          
          2:S:not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y))
             -->_3 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_2 not#(or(x,y)) -> c_5(and#(not(x),not(y)),not#(x),not#(y)):2
             -->_3 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          not#(or(x,y)) -> c_5(not#(x),not#(y))
** Step 4.b:3: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(not#(x),not#(y))
        - Weak TRS:
            and(x,or(y,z)) -> or(and(x,y),and(x,z))
            and(or(y,z),x) -> or(and(x,y),and(x,z))
            not(and(x,y)) -> or(not(x),not(y))
            not(not(x)) -> x
            not(or(x,y)) -> and(not(x),not(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          not#(and(x,y)) -> c_3(not#(x),not#(y))
          not#(or(x,y)) -> c_5(not#(x),not#(y))
** Step 4.b:4: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(not#(x),not#(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: not#(and(x,y)) -> c_3(not#(x),not#(y))
          
        The strictly oriented rules are moved into the weak component.
*** Step 4.b:4.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(not#(x),not#(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_3) = {1,2},
          uargs(c_5) = {1,2}
        
        Following symbols are considered usable:
          {and#,not#}
        TcT has computed the following interpretation:
           p(and) = [13] x1 + [4] x2 + [2]
           p(not) = [0]                   
            p(or) = [1] x1 + [1] x2 + [0] 
          p(and#) = [2] x1 + [1] x2 + [8] 
          p(not#) = [1] x1 + [0]          
           p(c_1) = [1]                   
           p(c_2) = [1] x1 + [1] x2 + [8] 
           p(c_3) = [4] x1 + [4] x2 + [0] 
           p(c_4) = [0]                   
           p(c_5) = [1] x1 + [1] x2 + [0] 
        
        Following rules are strictly oriented:
        not#(and(x,y)) = [13] x + [4] y + [2]
                       > [4] x + [4] y + [0] 
                       = c_3(not#(x),not#(y))
        
        
        Following rules are (at-least) weakly oriented:
        not#(or(x,y)) =  [1] x + [1] y + [0] 
                      >= [1] x + [1] y + [0] 
                      =  c_5(not#(x),not#(y))
        
*** Step 4.b:4.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            not#(or(x,y)) -> c_5(not#(x),not#(y))
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

*** Step 4.b:4.b:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            not#(or(x,y)) -> c_5(not#(x),not#(y))
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: not#(or(x,y)) -> c_5(not#(x),not#(y))
          
        The strictly oriented rules are moved into the weak component.
**** Step 4.b:4.b:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            not#(or(x,y)) -> c_5(not#(x),not#(y))
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_3) = {1,2},
          uargs(c_5) = {1,2}
        
        Following symbols are considered usable:
          {and#,not#}
        TcT has computed the following interpretation:
           p(and) = [1] x1 + [1] x2 + [0] 
           p(not) = [1]                   
            p(or) = [1] x1 + [1] x2 + [3] 
          p(and#) = [0]                   
          p(not#) = [8] x1 + [0]          
           p(c_1) = [1] x1 + [8] x2 + [1] 
           p(c_2) = [8] x2 + [2]          
           p(c_3) = [1] x1 + [1] x2 + [0] 
           p(c_4) = [1]                   
           p(c_5) = [1] x1 + [1] x2 + [12]
        
        Following rules are strictly oriented:
        not#(or(x,y)) = [8] x + [8] y + [24]
                      > [8] x + [8] y + [12]
                      = c_5(not#(x),not#(y))
        
        
        Following rules are (at-least) weakly oriented:
        not#(and(x,y)) =  [8] x + [8] y + [0] 
                       >= [8] x + [8] y + [0] 
                       =  c_3(not#(x),not#(y))
        
**** Step 4.b:4.b:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(not#(x),not#(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 4.b:4.b:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            not#(and(x,y)) -> c_3(not#(x),not#(y))
            not#(or(x,y)) -> c_5(not#(x),not#(y))
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:not#(and(x,y)) -> c_3(not#(x),not#(y))
             -->_2 not#(or(x,y)) -> c_5(not#(x),not#(y)):2
             -->_1 not#(or(x,y)) -> c_5(not#(x),not#(y)):2
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
             -->_1 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
          
          2:W:not#(or(x,y)) -> c_5(not#(x),not#(y))
             -->_2 not#(or(x,y)) -> c_5(not#(x),not#(y)):2
             -->_1 not#(or(x,y)) -> c_5(not#(x),not#(y)):2
             -->_2 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
             -->_1 not#(and(x,y)) -> c_3(not#(x),not#(y)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: not#(and(x,y)) -> c_3(not#(x),not#(y))
          2: not#(or(x,y)) -> c_5(not#(x),not#(y))
**** Step 4.b:4.b:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {and/2,not/1,and#/2,not#/1} / {or/2,c_1/2,c_2/2,c_3/2,c_4/0,c_5/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and#,not#} and constructors {or}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

MAYBE