/export/starexec/sandbox2/solver/bin/starexec_run_tct_dci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^2))
* Step 1: NaturalMI.  WORST_CASE(?,O(n^2))
    + 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 derivational complexity wrt. signature {implies,not,or}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind triangular matrix interpretation:
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(implies) = [1] x1 + [1] x2 + [0]
              p(not) = [1] x1 + [1]         
               p(or) = [1] x1 + [1] x2 + [0]
        
        Following rules are strictly oriented:
              implies(not(x),y) = [1] x + [1] y + [1]        
                                > [1] x + [1] y + [0]        
                                = or(x,y)                    
        
        implies(not(x),or(y,z)) = [1] x + [1] y + [1] z + [1]
                                > [1] x + [1] y + [1] z + [0]
                                = implies(y,or(x,z))         
        
        
        Following rules are (at-least) weakly oriented:
        implies(x,or(y,z)) =  [1] x + [1] y + [1] z + [0]
                           >= [1] x + [1] y + [1] z + [0]
                           =  or(y,implies(x,z))         
        
* Step 2: NaturalMI.  WORST_CASE(?,O(n^2))
    + 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 derivational complexity wrt. signature {implies,not,or}
    + Applied Processor:
        NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind triangular matrix interpretation:
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(implies) = [1 0] x1 + [1 1] x2 + [0]
                       [0 1]      [0 1]      [0]
              p(not) = [1 4] x1 + [3]           
                       [0 1]      [4]           
               p(or) = [1 2] x1 + [1 0] x2 + [1]
                       [0 1]      [0 1]      [2]
        
        Following rules are strictly oriented:
        implies(x,or(y,z)) = [1 0] x + [1 3] y + [1 1] z + [3]
                             [0 1]     [0 1]     [0 1]     [2]
                           > [1 0] x + [1 2] y + [1 1] z + [1]
                             [0 1]     [0 1]     [0 1]     [2]
                           = or(y,implies(x,z))               
        
        
        Following rules are (at-least) weakly oriented:
              implies(not(x),y) =  [1 4] x + [1 1] y + [3]          
                                   [0 1]     [0 1]     [4]          
                                >= [1 2] x + [1 0] y + [1]          
                                   [0 1]     [0 1]     [2]          
                                =  or(x,y)                          
        
        implies(not(x),or(y,z)) =  [1 4] x + [1 3] y + [1 1] z + [6]
                                   [0 1]     [0 1]     [0 1]     [6]
                                >= [1 3] x + [1 0] y + [1 1] z + [3]
                                   [0 1]     [0 1]     [0 1]     [2]
                                =  implies(y,or(x,z))               
        
* Step 3: 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 derivational complexity wrt. signature {implies,not,or}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))