WORST_CASE(?,O(n^2))
* Step 1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,*(y,z)) -> *(otimes(x,y),z)
            *(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,otimes/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus,otimes}
    + 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*x1 + x1*x2 + x2
               p(+) = 2 + x1 + x2      
               p(1) = 0                
           p(oplus) = 2 + x1 + x2      
          p(otimes) = 0                
        
        Following rules are strictly oriented:
        *(+(x,y),z) = 4 + 2*x + x*z + 2*y + y*z + 3*z
                    > 2 + 2*x + x*z + 2*y + y*z + 2*z
                    = oplus(*(x,z),*(y,z))           
        
        
        Following rules are (at-least) weakly oriented:
            *(x,*(y,z)) =  2*x + 2*x*y + x*y*z + x*z + 2*y + y*z + z
                        >= z                                        
                        =  *(otimes(x,y),z)                         
        
        *(x,oplus(y,z)) =  2 + 4*x + x*y + x*z + y + z              
                        >= 2 + 4*x + x*y + 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,*(y,z)) -> *(otimes(x,y),z)
            *(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,otimes/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus,otimes}
    + 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(*) = x1 + 2*x1*x2 + 2*x2
               p(+) = 1 + x1 + x2        
               p(1) = 0                  
           p(oplus) = 1 + x1 + x2        
          p(otimes) = 0                  
        
        Following rules are strictly oriented:
        *(x,oplus(y,z)) = 2 + 3*x + 2*x*y + 2*x*z + 2*y + 2*z
                        > 1 + 2*x + 2*x*y + 2*x*z + 2*y + 2*z
                        = oplus(*(x,y),*(x,z))               
        
        
        Following rules are (at-least) weakly oriented:
        *(x,*(y,z)) =  x + 2*x*y + 4*x*y*z + 4*x*z + 2*y + 4*y*z + 4*z
                    >= 2*z                                            
                    =  *(otimes(x,y),z)                               
        
        *(+(x,y),z) =  1 + x + 2*x*z + y + 2*y*z + 4*z                
                    >= 1 + x + 2*x*z + y + 2*y*z + 4*z                
                    =  oplus(*(x,z),*(y,z))                           
        
           *(1(),y) =  2*y                                            
                    >= y                                              
                    =  y                                              
        
* Step 3: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,*(y,z)) -> *(otimes(x,y),z)
            *(1(),y) -> y
        - Weak TRS:
            *(x,oplus(y,z)) -> oplus(*(x,y),*(x,z))
            *(+(x,y),z) -> oplus(*(x,z),*(y,z))
        - Signature:
            {*/2} / {+/2,1/0,oplus/2,otimes/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus,otimes}
    + 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*x1 + 3*x1*x2 + x2
               p(+) = 2 + x1 + x2        
               p(1) = 1                  
           p(oplus) = 3 + x1 + x2        
          p(otimes) = x2                 
        
        Following rules are strictly oriented:
        *(1(),y) = 2 + 4*y
                 > y      
                 = y      
        
        
        Following rules are (at-least) weakly oriented:
            *(x,*(y,z)) =  2*x + 6*x*y + 9*x*y*z + 3*x*z + 2*y + 3*y*z + z
                        >= 2*y + 3*y*z + z                                
                        =  *(otimes(x,y),z)                               
        
        *(x,oplus(y,z)) =  3 + 11*x + 3*x*y + 3*x*z + y + z               
                        >= 3 + 4*x + 3*x*y + 3*x*z + y + z                
                        =  oplus(*(x,y),*(x,z))                           
        
            *(+(x,y),z) =  4 + 2*x + 3*x*z + 2*y + 3*y*z + 7*z            
                        >= 3 + 2*x + 3*x*z + 2*y + 3*y*z + 2*z            
                        =  oplus(*(x,z),*(y,z))                           
        
* Step 4: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(x,*(y,z)) -> *(otimes(x,y),z)
        - 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,otimes/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus,otimes}
    + 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(*) = 1 + 2*x1 + 2*x1*x2 + 2*x2
               p(+) = 2 + x1 + x2              
               p(1) = 0                        
           p(oplus) = 1 + x1 + x2              
          p(otimes) = 0                        
        
        Following rules are strictly oriented:
        *(x,*(y,z)) = 3 + 4*x + 4*x*y + 4*x*y*z + 4*x*z + 4*y + 4*y*z + 4*z
                    > 1 + 2*z                                              
                    = *(otimes(x,y),z)                                     
        
        
        Following rules are (at-least) weakly oriented:
        *(x,oplus(y,z)) =  3 + 4*x + 2*x*y + 2*x*z + 2*y + 2*z
                        >= 3 + 4*x + 2*x*y + 2*x*z + 2*y + 2*z
                        =  oplus(*(x,y),*(x,z))               
        
            *(+(x,y),z) =  5 + 2*x + 2*x*z + 2*y + 2*y*z + 6*z
                        >= 3 + 2*x + 2*x*z + 2*y + 2*y*z + 4*z
                        =  oplus(*(x,z),*(y,z))               
        
               *(1(),y) =  1 + 2*y                            
                        >= y                                  
                        =  y                                  
        
* Step 5: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            *(x,*(y,z)) -> *(otimes(x,y),z)
            *(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,otimes/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {+,1,oplus,otimes}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))