WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          merge(y,++(u(),v())){y -> ++(x,y)} =
            merge(++(x,y),++(u(),v())) ->^+ ++(x,merge(y,++(u(),v())))
              = C[merge(y,++(u(),v())) = merge(y,++(u(),v())){}]

** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,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}
        
        Following symbols are considered usable:
          {merge}
        TcT has computed the following interpretation:
             p(++) = 9 + x2     
          p(merge) = 2 + x1 + x2
            p(nil) = 3          
              p(u) = 0          
              p(v) = 11         
        
        Following rules are strictly oriented:
        merge(x,nil()) = 5 + x
                       > x    
                       = x    
        
        merge(nil(),y) = 5 + y
                       > y    
                       = y    
        
        
        Following rules are (at-least) weakly oriented:
        merge(++(x,y),++(u(),v())) =  31 + y                    
                                   >= 31 + y                    
                                   =  ++(x,merge(y,++(u(),v())))
        
        merge(++(x,y),++(u(),v())) =  31 + y                    
                                   >= 31 + y                    
                                   =  ++(u(),merge(++(x,y),v()))
        
** Step 1.b:2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
        - Weak TRS:
            merge(x,nil()) -> x
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,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}
        
        Following symbols are considered usable:
          {merge}
        TcT has computed the following interpretation:
             p(++) = 2 + x1 + x2
          p(merge) = 8*x1 + x2  
            p(nil) = 0          
              p(u) = 0          
              p(v) = 0          
        
        Following rules are strictly oriented:
        merge(++(x,y),++(u(),v())) = 18 + 8*x + 8*y            
                                   > 4 + x + 8*y               
                                   = ++(x,merge(y,++(u(),v())))
        
        
        Following rules are (at-least) weakly oriented:
                    merge(x,nil()) =  8*x                       
                                   >= x                         
                                   =  x                         
        
        merge(++(x,y),++(u(),v())) =  18 + 8*x + 8*y            
                                   >= 18 + 8*x + 8*y            
                                   =  ++(u(),merge(++(x,y),v()))
        
                    merge(nil(),y) =  y                         
                                   >= y                         
                                   =  y                         
        
** Step 1.b:3: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
        - Weak TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,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}
        
        Following symbols are considered usable:
          {merge}
        TcT has computed the following interpretation:
             p(++) = 1 + x1 + x2    
          p(merge) = 1 + 8*x1 + 2*x2
            p(nil) = 0              
              p(u) = 10             
              p(v) = 0              
        
        Following rules are strictly oriented:
        merge(++(x,y),++(u(),v())) = 31 + 8*x + 8*y            
                                   > 20 + 8*x + 8*y            
                                   = ++(u(),merge(++(x,y),v()))
        
        
        Following rules are (at-least) weakly oriented:
                    merge(x,nil()) =  1 + 8*x                   
                                   >= x                         
                                   =  x                         
        
        merge(++(x,y),++(u(),v())) =  31 + 8*x + 8*y            
                                   >= 24 + x + 8*y              
                                   =  ++(x,merge(y,++(u(),v())))
        
                    merge(nil(),y) =  1 + 2*y                   
                                   >= y                         
                                   =  y                         
        
** Step 1.b:4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            merge(x,nil()) -> x
            merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
            merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
            merge(nil(),y) -> y
        - Signature:
            {merge/2} / {++/2,nil/0,u/0,v/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))