WORST_CASE(?,O(n^1))
* Step 1: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            implies(x,or(y,z)) -> or(y,implies(x,z))
            implies(not(x),y) -> or(x,y)
            implies(not(x),or(y,z)) -> implies(y,or(x,z))
        - Signature:
            {implies/2} / {not/1,or/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        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(or) = {2}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
            p(implies) = [2] x2 + [9]
                p(not) = [1] x1 + [0]
                 p(or) = [1] x2 + [0]
          
          Following rules are strictly oriented:
          implies(not(x),y) = [2] y + [9]
                            > [1] y + [0]
                            = or(x,y)    
          
          
          Following rules are (at-least) weakly oriented:
               implies(x,or(y,z)) =  [2] z + [9]       
                                  >= [2] z + [9]       
                                  =  or(y,implies(x,z))
          
          implies(not(x),or(y,z)) =  [2] z + [9]       
                                  >= [2] z + [9]       
                                  =  implies(y,or(x,z))
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            implies(x,or(y,z)) -> or(y,implies(x,z))
            implies(not(x),or(y,z)) -> implies(y,or(x,z))
        - Weak TRS:
            implies(not(x),y) -> or(x,y)
        - Signature:
            {implies/2} / {not/1,or/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or}
    + 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(or) = {2}
        
        Following symbols are considered usable:
          {implies}
        TcT has computed the following interpretation:
          p(implies) = [2] x1 + [2] x2 + [0]
              p(not) = [1] x1 + [9]         
               p(or) = [1] x1 + [1] x2 + [0]
        
        Following rules are strictly oriented:
        implies(not(x),or(y,z)) = [2] x + [2] y + [2] z + [18]
                                > [2] x + [2] y + [2] z + [0] 
                                = implies(y,or(x,z))          
        
        
        Following rules are (at-least) weakly oriented:
        implies(x,or(y,z)) =  [2] x + [2] y + [2] z + [0]
                           >= [2] x + [1] y + [2] z + [0]
                           =  or(y,implies(x,z))         
        
         implies(not(x),y) =  [2] x + [2] y + [18]       
                           >= [1] x + [1] y + [0]        
                           =  or(x,y)                    
        
* Step 3: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            implies(x,or(y,z)) -> or(y,implies(x,z))
        - Weak TRS:
            implies(not(x),y) -> or(x,y)
            implies(not(x),or(y,z)) -> implies(y,or(x,z))
        - Signature:
            {implies/2} / {not/1,or/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or}
    + 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(or) = {2}
        
        Following symbols are considered usable:
          {implies}
        TcT has computed the following interpretation:
          p(implies) = [2] x1 + [2] x2 + [4]
              p(not) = [1] x1 + [2]         
               p(or) = [1] x1 + [1] x2 + [8]
        
        Following rules are strictly oriented:
        implies(x,or(y,z)) = [2] x + [2] y + [2] z + [20]
                           > [2] x + [1] y + [2] z + [12]
                           = or(y,implies(x,z))          
        
        
        Following rules are (at-least) weakly oriented:
              implies(not(x),y) =  [2] x + [2] y + [8]         
                                >= [1] x + [1] y + [8]         
                                =  or(x,y)                     
        
        implies(not(x),or(y,z)) =  [2] x + [2] y + [2] z + [24]
                                >= [2] x + [2] y + [2] z + [20]
                                =  implies(y,or(x,z))          
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            implies(x,or(y,z)) -> or(y,implies(x,z))
            implies(not(x),y) -> or(x,y)
            implies(not(x),or(y,z)) -> implies(y,or(x,z))
        - Signature:
            {implies/2} / {not/1,or/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))