* Step 1: Sum WORST_CASE(Omega(n^1),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:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(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:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          implies(x,z){z -> or(y,z)} =
            implies(x,or(y,z)) ->^+ or(y,implies(x,z))
              = C[implies(x,z) = implies(x,z){}]

** Step 1.b:1: MI 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:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 1, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        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] x_2 + [10]
              p(not) = [0]           
               p(or) = [1] x_2 + [10]
        
        Following rules are strictly oriented:
        implies(x,or(y,z)) = [2] z + [30]      
                           > [2] z + [20]      
                           = or(y,implies(x,z))
        
        
        Following rules are (at-least) weakly oriented:
              implies(not(x),y) =  [2] y + [10]      
                                >= [1] y + [10]      
                                =  or(x,y)           
        
        implies(not(x),or(y,z)) =  [2] z + [30]      
                                >= [2] z + [30]      
                                =  implies(y,or(x,z))
        
** Step 1.b:2: MI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            implies(not(x),y) -> or(x,y)
            implies(not(x),or(y,z)) -> implies(y,or(x,z))
        - Weak TRS:
            implies(x,or(y,z)) -> or(y,implies(x,z))
        - Signature:
            {implies/2} / {not/1,or/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {implies} and constructors {not,or}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 1, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        The following argument positions are considered usable:
          uargs(or) = {2}
        
        Following symbols are considered usable:
          {implies}
        TcT has computed the following interpretation:
          p(implies) = [8] x_2 + [4]
              p(not) = [0]          
               p(or) = [1] x_2 + [0]
        
        Following rules are strictly oriented:
        implies(not(x),y) = [8] y + [4]
                          > [1] y + [0]
                          = or(x,y)    
        
        
        Following rules are (at-least) weakly oriented:
             implies(x,or(y,z)) =  [8] z + [4]       
                                >= [8] z + [4]       
                                =  or(y,implies(x,z))
        
        implies(not(x),or(y,z)) =  [8] z + [4]       
                                >= [8] z + [4]       
                                =  implies(y,or(x,z))
        
** Step 1.b:3: MI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            implies(not(x),or(y,z)) -> implies(y,or(x,z))
        - Weak TRS:
            implies(x,or(y,z)) -> or(y,implies(x,z))
            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:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 1, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        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] x_1 + [2] x_2 + [2]
              p(not) = [1] x_1 + [1]          
               p(or) = [1] x_1 + [1] x_2 + [0]
        
        Following rules are strictly oriented:
        implies(not(x),or(y,z)) = [2] x + [2] y + [2] z + [4]
                                > [2] x + [2] y + [2] z + [2]
                                = implies(y,or(x,z))         
        
        
        Following rules are (at-least) weakly oriented:
        implies(x,or(y,z)) =  [2] x + [2] y + [2] z + [2]
                           >= [2] x + [1] y + [2] z + [2]
                           =  or(y,implies(x,z))         
        
         implies(not(x),y) =  [2] x + [2] y + [4]        
                           >= [1] x + [1] y + [0]        
                           =  or(x,y)                    
        
** Step 1.b: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(Omega(n^1),O(n^1))