*** 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:
        Full
        basic terms: {and}/{band,not}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      We add the following weak dependency pairs:
      
      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:
        and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {and/3,and#/3} / {band/2,not/1,c_1/1}
      Obligation:
        Full
        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:
        Full
        basic terms: {and#}/{band,not}
    Applied Processor:
      WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    Proof:
      The weightgap principle applies using the following constant growth matrix-interpretation:
        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:
          {}
        TcT has computed the following interpretation:
           p(and) = [0]                  
          p(band) = [0]                  
           p(not) = [5]                  
          p(and#) = [4] x1 + [8] x2 + [8]
           p(c_1) = [1] x1 + [0]         
        
        Following rules are strictly oriented:
        and#(not(not(x)),y,not(z)) = [8] y + [28]            
                                   > [4] y + [8]             
                                   = c_1(and#(y,band(x,z),x))
        
        
        Following rules are (at-least) weakly oriented:
        
      Further, it can be verified that all rules not oriented are covered by the weightgap condition.
*** 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:
        Full
        basic terms: {and#}/{band,not}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).