*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        *(x,+(y,z)) -> +(*(x,y),*(x,z))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {*/2} / {+/2}
      Obligation:
        Innermost
        basic terms: {*}/{+}
    Applied Processor:
      WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    Proof:
      The weightgap principle applies using the following nonconstant growth matrix-interpretation:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(+) = {1,2}
        
        Following symbols are considered usable:
          {}
        TcT has computed the following interpretation:
          p(*) = [6] x2 + [1]         
          p(+) = [1] x1 + [1] x2 + [2]
        
        Following rules are strictly oriented:
        *(x,+(y,z)) = [6] y + [6] z + [13]
                    > [6] y + [6] z + [4] 
                    = +(*(x,y),*(x,z))    
        
        
        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 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        *(x,+(y,z)) -> +(*(x,y),*(x,z))
      Signature:
        {*/2} / {+/2}
      Obligation:
        Innermost
        basic terms: {*}/{+}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).