* Step 1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
            *(x,1()) -> x
            *(+(x,y),z) -> +(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*} and constructors {+,1}
    + Applied Processor:
        NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(mixed(2)):
        The following argument positions are considered usable:
          uargs(+) = {1,2}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(*) = x1 + 4*x1*x2 + 2*x2
          p(+) = 1 + x1 + x2        
          p(1) = 0                  
        
        Following rules are strictly oriented:
        *(x,+(y,z)) = 2 + 5*x + 4*x*y + 4*x*z + 2*y + 2*z
                    > 1 + 2*x + 4*x*y + 4*x*z + 2*y + 2*z
                    = +(*(x,y),*(x,z))                   
        
        
        Following rules are (at-least) weakly oriented:
           *(x,1()) =  x                              
                    >= x                              
                    =  x                              
        
        *(+(x,y),z) =  1 + x + 4*x*z + y + 4*y*z + 6*z
                    >= 1 + x + 4*x*z + y + 4*y*z + 4*z
                    =  +(*(x,z),*(y,z))               
        
           *(1(),y) =  2*y                            
                    >= y                              
                    =  y                              
        
* Step 2: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,1()) -> x
            *(+(x,y),z) -> +(*(x,z),*(y,z))
            *(1(),y) -> y
        - Weak TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
        - Signature:
            {*/2} / {+/2,1/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*} and constructors {+,1}
    + Applied Processor:
        NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(mixed(2)):
        The following argument positions are considered usable:
          uargs(+) = {1,2}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(*) = 2*x1 + 2*x1*x2 + x2
          p(+) = 1 + x1 + x2        
          p(1) = 0                  
        
        Following rules are strictly oriented:
        *(+(x,y),z) = 2 + 2*x + 2*x*z + 2*y + 2*y*z + 3*z
                    > 1 + 2*x + 2*x*z + 2*y + 2*y*z + 2*z
                    = +(*(x,z),*(y,z))                   
        
        
        Following rules are (at-least) weakly oriented:
        *(x,+(y,z)) =  1 + 4*x + 2*x*y + 2*x*z + y + z
                    >= 1 + 4*x + 2*x*y + 2*x*z + y + z
                    =  +(*(x,y),*(x,z))               
        
           *(x,1()) =  2*x                            
                    >= x                              
                    =  x                              
        
           *(1(),y) =  y                              
                    >= y                              
                    =  y                              
        
* Step 3: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,1()) -> x
            *(1(),y) -> y
        - Weak TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
            *(+(x,y),z) -> +(*(x,z),*(y,z))
        - Signature:
            {*/2} / {+/2,1/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*} and constructors {+,1}
    + Applied Processor:
        NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(mixed(2)):
        The following argument positions are considered usable:
          uargs(+) = {1,2}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(*) = 2 + 7*x1 + 7*x1*x2 + 6*x2
          p(+) = 1 + x1 + x2              
          p(1) = 1                        
        
        Following rules are strictly oriented:
        *(x,1()) = 8 + 14*x
                 > x       
                 = x       
        
        *(1(),y) = 9 + 13*y
                 > y       
                 = y       
        
        
        Following rules are (at-least) weakly oriented:
        *(x,+(y,z)) =  8 + 14*x + 7*x*y + 7*x*z + 6*y + 6*z
                    >= 5 + 14*x + 7*x*y + 7*x*z + 6*y + 6*z
                    =  +(*(x,y),*(x,z))                    
        
        *(+(x,y),z) =  9 + 7*x + 7*x*z + 7*y + 7*y*z + 13*z
                    >= 5 + 7*x + 7*x*z + 7*y + 7*y*z + 12*z
                    =  +(*(x,z),*(y,z))                    
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
            *(x,1()) -> x
            *(+(x,y),z) -> +(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*} and constructors {+,1}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))