WORST_CASE(?,O(n^1))
* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            =(.(x,y),.(u(),v())) -> and(=(x,u()),=(y,v()))
            =(.(x,y),nil()) -> false()
            =(nil(),.(y,z)) -> false()
            =(nil(),nil()) -> true()
            del(.(x,.(y,z))) -> f(=(x,y),x,y,z)
            f(false(),x,y,z) -> .(x,del(.(y,z)))
            f(true(),x,y,z) -> del(.(y,z))
        - Signature:
            {=/2,del/1,f/4} / {./2,and/2,false/0,nil/0,true/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {=,del,f} and constructors {.,and,false,nil,true,u,v}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            =(.(x,y),.(u(),v())) -> and(=(x,u()),=(y,v()))
            =(.(x,y),nil()) -> false()
            =(nil(),.(y,z)) -> false()
            =(nil(),nil()) -> true()
            del(.(x,.(y,z))) -> f(=(x,y),x,y,z)
            f(false(),x,y,z) -> .(x,del(.(y,z)))
            f(true(),x,y,z) -> del(.(y,z))
        - Signature:
            {=/2,del/1,f/4} / {./2,and/2,false/0,nil/0,true/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {=,del,f} and constructors {.,and,false,nil,true,u,v}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(.) = {2},
          uargs(f) = {1}
        
        Following symbols are considered usable:
          {=,del,f}
        TcT has computed the following interpretation:
              p(.) = 2 + x2         
              p(=) = 1              
            p(and) = 0              
            p(del) = 6 + 4*x1       
              p(f) = 8 + 8*x1 + 4*x4
          p(false) = 1              
            p(nil) = 0              
           p(true) = 1              
              p(u) = 1              
              p(v) = 0              
        
        Following rules are strictly oriented:
        =(.(x,y),.(u(),v())) = 1                     
                             > 0                     
                             = and(=(x,u()),=(y,v()))
        
            del(.(x,.(y,z))) = 22 + 4*z              
                             > 16 + 4*z              
                             = f(=(x,y),x,y,z)       
        
             f(true(),x,y,z) = 16 + 4*z              
                             > 14 + 4*z              
                             = del(.(y,z))           
        
        
        Following rules are (at-least) weakly oriented:
         =(.(x,y),nil()) =  1               
                         >= 1               
                         =  false()         
        
         =(nil(),.(y,z)) =  1               
                         >= 1               
                         =  false()         
        
          =(nil(),nil()) =  1               
                         >= 1               
                         =  true()          
        
        f(false(),x,y,z) =  16 + 4*z        
                         >= 16 + 4*z        
                         =  .(x,del(.(y,z)))
        
* Step 3: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            =(.(x,y),nil()) -> false()
            =(nil(),.(y,z)) -> false()
            =(nil(),nil()) -> true()
            f(false(),x,y,z) -> .(x,del(.(y,z)))
        - Weak TRS:
            =(.(x,y),.(u(),v())) -> and(=(x,u()),=(y,v()))
            del(.(x,.(y,z))) -> f(=(x,y),x,y,z)
            f(true(),x,y,z) -> del(.(y,z))
        - Signature:
            {=/2,del/1,f/4} / {./2,and/2,false/0,nil/0,true/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {=,del,f} and constructors {.,and,false,nil,true,u,v}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(.) = {2},
          uargs(f) = {1}
        
        Following symbols are considered usable:
          {=,del,f}
        TcT has computed the following interpretation:
              p(.) = 4 + x2     
              p(=) = 4          
            p(and) = 0          
            p(del) = 2 + 2*x1   
              p(f) = 4*x1 + 2*x4
          p(false) = 4          
            p(nil) = 2          
           p(true) = 3          
              p(u) = 2          
              p(v) = 8          
        
        Following rules are strictly oriented:
          =(nil(),nil()) = 4               
                         > 3               
                         = true()          
        
        f(false(),x,y,z) = 16 + 2*z        
                         > 14 + 2*z        
                         = .(x,del(.(y,z)))
        
        
        Following rules are (at-least) weakly oriented:
        =(.(x,y),.(u(),v())) =  4                     
                             >= 0                     
                             =  and(=(x,u()),=(y,v()))
        
             =(.(x,y),nil()) =  4                     
                             >= 4                     
                             =  false()               
        
             =(nil(),.(y,z)) =  4                     
                             >= 4                     
                             =  false()               
        
            del(.(x,.(y,z))) =  18 + 2*z              
                             >= 16 + 2*z              
                             =  f(=(x,y),x,y,z)       
        
             f(true(),x,y,z) =  12 + 2*z              
                             >= 10 + 2*z              
                             =  del(.(y,z))           
        
* Step 4: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            =(.(x,y),nil()) -> false()
            =(nil(),.(y,z)) -> false()
        - Weak TRS:
            =(.(x,y),.(u(),v())) -> and(=(x,u()),=(y,v()))
            =(nil(),nil()) -> true()
            del(.(x,.(y,z))) -> f(=(x,y),x,y,z)
            f(false(),x,y,z) -> .(x,del(.(y,z)))
            f(true(),x,y,z) -> del(.(y,z))
        - Signature:
            {=/2,del/1,f/4} / {./2,and/2,false/0,nil/0,true/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {=,del,f} and constructors {.,and,false,nil,true,u,v}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(.) = {2},
          uargs(f) = {1}
        
        Following symbols are considered usable:
          {=,del,f}
        TcT has computed the following interpretation:
              p(.) = 4 + x1 + x2                 
              p(=) = 1                           
            p(and) = 0                           
            p(del) = 1 + 2*x1                    
              p(f) = 13 + 2*x1 + x2 + 2*x3 + 2*x4
          p(false) = 0                           
            p(nil) = 1                           
           p(true) = 1                           
              p(u) = 10                          
              p(v) = 3                           
        
        Following rules are strictly oriented:
        =(.(x,y),nil()) = 1      
                        > 0      
                        = false()
        
        =(nil(),.(y,z)) = 1      
                        > 0      
                        = false()
        
        
        Following rules are (at-least) weakly oriented:
        =(.(x,y),.(u(),v())) =  1                     
                             >= 0                     
                             =  and(=(x,u()),=(y,v()))
        
              =(nil(),nil()) =  1                     
                             >= 1                     
                             =  true()                
        
            del(.(x,.(y,z))) =  17 + 2*x + 2*y + 2*z  
                             >= 15 + x + 2*y + 2*z    
                             =  f(=(x,y),x,y,z)       
        
            f(false(),x,y,z) =  13 + x + 2*y + 2*z    
                             >= 13 + x + 2*y + 2*z    
                             =  .(x,del(.(y,z)))      
        
             f(true(),x,y,z) =  15 + x + 2*y + 2*z    
                             >= 9 + 2*y + 2*z         
                             =  del(.(y,z))           
        
* Step 5: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            =(.(x,y),.(u(),v())) -> and(=(x,u()),=(y,v()))
            =(.(x,y),nil()) -> false()
            =(nil(),.(y,z)) -> false()
            =(nil(),nil()) -> true()
            del(.(x,.(y,z))) -> f(=(x,y),x,y,z)
            f(false(),x,y,z) -> .(x,del(.(y,z)))
            f(true(),x,y,z) -> del(.(y,z))
        - Signature:
            {=/2,del/1,f/4} / {./2,and/2,false/0,nil/0,true/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {=,del,f} and constructors {.,and,false,nil,true,u,v}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))