*** 1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {and/3} / {band/2,not/1}
      Obligation:
        Innermost
        basic terms: {and}/{band,not}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      We add the following dependency tuples:
      
      Strict DPs
        and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
      Weak DPs
        
      
      and mark the set of starting terms.
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)
      Signature:
        {and/3,and#/3} / {band/2,not/1,c_1/1}
      Obligation:
        Innermost
        basic terms: {and#}/{band,not}
    Applied Processor:
      UsableRules
    Proof:
      We replace rewrite rules by usable rules:
        and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {and/3,and#/3} / {band/2,not/1,c_1/1}
      Obligation:
        Innermost
        basic terms: {and#}/{band,not}
    Applied Processor:
      NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules, greedy = NoGreedy}
    Proof:
      We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
      The following argument positions are considered usable:
        uargs(c_1) = {1}
      
      Following symbols are considered usable:
        {and#}
      TcT has computed the following interpretation:
         p(and) = [1] x1 + [1] x2 + [2] x3 + [1]
        p(band) = [0]                           
         p(not) = [4]                           
        p(and#) = [4] x1 + [8] x2 + [3]         
         p(c_1) = [1] x1 + [12]                 
      
      Following rules are strictly oriented:
      and#(not(not(x)),y,not(z)) = [8] y + [19]            
                                 > [4] y + [15]            
                                 = c_1(and#(y,band(x,z),x))
      
      
      Following rules are (at-least) weakly oriented:
      
*** 1.1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        and#(not(not(x)),y,not(z)) -> c_1(and#(y,band(x,z),x))
      Weak TRS Rules:
        
      Signature:
        {and/3,and#/3} / {band/2,not/1,c_1/1}
      Obligation:
        Innermost
        basic terms: {and#}/{band,not}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).