* Step 1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))
            *(+(x,y),z) -> oplus(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0,oplus/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus}
    + 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(oplus) = {1,2}
        
        Following symbols are considered usable:
          {*}
        TcT has computed the following interpretation:
              p(*) = 3*x1 + 5*x1*x2 + x2
              p(+) = 1 + x1 + x2        
              p(1) = 0                  
          p(oplus) = 1 + x1 + x2        
        
        Following rules are strictly oriented:
        *(+(x,y),z) = 3 + 3*x + 5*x*z + 3*y + 5*y*z + 6*z
                    > 1 + 3*x + 5*x*z + 3*y + 5*y*z + 2*z
                    = oplus(*(x,z),*(y,z))               
        
        
        Following rules are (at-least) weakly oriented:
        *(x,oplus(y,z)) =  1 + 8*x + 5*x*y + 5*x*z + y + z
                        >= 1 + 6*x + 5*x*y + 5*x*z + y + z
                        =  oplus(*(x,y),*(x,z))           
        
               *(1(),y) =  y                              
                        >= y                              
                        =  y                              
        
* Step 2: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))
            *(1(),y) -> y
        - Weak TRS:
            *(+(x,y),z) -> oplus(*(x,z),*(y,z))
        - Signature:
            {*/2} / {+/2,1/0,oplus/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus}
    + 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(oplus) = {1,2}
        
        Following symbols are considered usable:
          {*}
        TcT has computed the following interpretation:
              p(*) = 2 + 5*x1 + 6*x1*x2 + 6*x2
              p(+) = 1 + x1 + x2              
              p(1) = 0                        
          p(oplus) = 1 + x1 + x2              
        
        Following rules are strictly oriented:
        *(x,oplus(y,z)) = 8 + 11*x + 6*x*y + 6*x*z + 6*y + 6*z
                        > 5 + 10*x + 6*x*y + 6*x*z + 6*y + 6*z
                        = oplus(*(x,y),*(x,z))                
        
               *(1(),y) = 2 + 6*y                             
                        > y                                   
                        = y                                   
        
        
        Following rules are (at-least) weakly oriented:
        *(+(x,y),z) =  7 + 5*x + 6*x*z + 5*y + 6*y*z + 12*z
                    >= 5 + 5*x + 6*x*z + 5*y + 6*y*z + 12*z
                    =  oplus(*(x,z),*(y,z))                
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))
            *(+(x,y),z) -> oplus(*(x,z),*(y,z))
            *(1(),y) -> y
        - Signature:
            {*/2} / {+/2,1/0,oplus/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))