WORST_CASE(Omega(n^1),O(n^3))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^3))
    + Considered Problem:
        - Strict TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            goal(xs,ys) -> mul0(xs,ys)
            isZero(C(x,y)) -> False()
            isZero(Z()) -> True()
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
            second(C(x,y)) -> y
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1} / {C/2,False/0,S/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,isZero,mul0,second} and constructors {C,False,S
            ,True,Z}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            goal(xs,ys) -> mul0(xs,ys)
            isZero(C(x,y)) -> False()
            isZero(Z()) -> True()
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
            second(C(x,y)) -> y
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1} / {C/2,False/0,S/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,isZero,mul0,second} and constructors {C,False,S
            ,True,Z}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          add0(y,z){y -> C(x,y)} =
            add0(C(x,y),z) ->^+ add0(y,C(S(),z))
              = C[add0(y,C(S(),z)) = add0(y,z){z -> C(S(),z)}]

** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            goal(xs,ys) -> mul0(xs,ys)
            isZero(C(x,y)) -> False()
            isZero(Z()) -> True()
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
            second(C(x,y)) -> y
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1} / {C/2,False/0,S/0,True/0,Z/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0,goal,isZero,mul0,second} and constructors {C,False,S
            ,True,Z}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
          add0#(Z(),y) -> c_2()
          goal#(xs,ys) -> c_3(mul0#(xs,ys))
          isZero#(C(x,y)) -> c_4()
          isZero#(Z()) -> c_5()
          mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
          mul0#(Z(),y) -> c_7()
          second#(C(x,y)) -> c_8()
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict DPs:
            add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
            add0#(Z(),y) -> c_2()
            goal#(xs,ys) -> c_3(mul0#(xs,ys))
            isZero#(C(x,y)) -> c_4()
            isZero#(Z()) -> c_5()
            mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
            mul0#(Z(),y) -> c_7()
            second#(C(x,y)) -> c_8()
        - Weak TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            goal(xs,ys) -> mul0(xs,ys)
            isZero(C(x,y)) -> False()
            isZero(Z()) -> True()
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
            second(C(x,y)) -> y
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/2,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,4,5,7,8}
        by application of
          Pre({2,4,5,7,8}) = {1,3,6}.
        Here rules are labelled as follows:
          1: add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
          2: add0#(Z(),y) -> c_2()
          3: goal#(xs,ys) -> c_3(mul0#(xs,ys))
          4: isZero#(C(x,y)) -> c_4()
          5: isZero#(Z()) -> c_5()
          6: mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
          7: mul0#(Z(),y) -> c_7()
          8: second#(C(x,y)) -> c_8()
** Step 1.b:3: RemoveWeakSuffixes WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict DPs:
            add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
            goal#(xs,ys) -> c_3(mul0#(xs,ys))
            mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
        - Weak DPs:
            add0#(Z(),y) -> c_2()
            isZero#(C(x,y)) -> c_4()
            isZero#(Z()) -> c_5()
            mul0#(Z(),y) -> c_7()
            second#(C(x,y)) -> c_8()
        - Weak TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            goal(xs,ys) -> mul0(xs,ys)
            isZero(C(x,y)) -> False()
            isZero(Z()) -> True()
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
            second(C(x,y)) -> y
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/2,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
             -->_1 add0#(Z(),y) -> c_2():4
             -->_1 add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y'))):1
          
          2:S:goal#(xs,ys) -> c_3(mul0#(xs,ys))
             -->_1 mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y')):3
             -->_1 mul0#(Z(),y) -> c_7():7
          
          3:S:mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
             -->_2 mul0#(Z(),y) -> c_7():7
             -->_1 add0#(Z(),y) -> c_2():4
             -->_2 mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y')):3
             -->_1 add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y'))):1
          
          4:W:add0#(Z(),y) -> c_2()
             
          
          5:W:isZero#(C(x,y)) -> c_4()
             
          
          6:W:isZero#(Z()) -> c_5()
             
          
          7:W:mul0#(Z(),y) -> c_7()
             
          
          8:W:second#(C(x,y)) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: second#(C(x,y)) -> c_8()
          6: isZero#(Z()) -> c_5()
          5: isZero#(C(x,y)) -> c_4()
          7: mul0#(Z(),y) -> c_7()
          4: add0#(Z(),y) -> c_2()
** Step 1.b:4: RemoveHeads WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict DPs:
            add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
            goal#(xs,ys) -> c_3(mul0#(xs,ys))
            mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
        - Weak TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            goal(xs,ys) -> mul0(xs,ys)
            isZero(C(x,y)) -> False()
            isZero(Z()) -> True()
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
            second(C(x,y)) -> y
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/2,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
           -->_1 add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y'))):1
        
        2:S:goal#(xs,ys) -> c_3(mul0#(xs,ys))
           -->_1 mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y')):3
        
        3:S:mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
           -->_2 mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y')):3
           -->_1 add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y'))):1
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(2,goal#(xs,ys) -> c_3(mul0#(xs,ys)))]
** Step 1.b:5: UsableRules WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict DPs:
            add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
            mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
        - Weak TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            goal(xs,ys) -> mul0(xs,ys)
            isZero(C(x,y)) -> False()
            isZero(Z()) -> True()
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
            second(C(x,y)) -> y
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/2,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          add0(C(x,y),y') -> add0(y,C(S(),y'))
          add0(Z(),y) -> y
          mul0(C(x,y),y') -> add0(mul0(y,y'),y')
          mul0(Z(),y) -> Z()
          add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
          mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
** Step 1.b:6: DecomposeDG WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict DPs:
            add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
            mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
        - Weak TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/2,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Nothing, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
        and a lower component
          add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
        Further, following extension rules are added to the lower component.
          mul0#(C(x,y),y') -> add0#(mul0(y,y'),y')
          mul0#(C(x,y),y') -> mul0#(y,y')
*** Step 1.b:6.a:1: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
        - Weak TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/2,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y'))
             -->_2 mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y')):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          mul0#(C(x,y),y') -> c_6(mul0#(y,y'))
*** Step 1.b:6.a:2: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            mul0#(C(x,y),y') -> c_6(mul0#(y,y'))
        - Weak TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          mul0#(C(x,y),y') -> c_6(mul0#(y,y'))
*** Step 1.b:6.a:3: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            mul0#(C(x,y),y') -> c_6(mul0#(y,y'))
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_6) = {1}
        
        Following symbols are considered usable:
          {add0#,goal#,isZero#,mul0#,second#}
        TcT has computed the following interpretation:
                p(C) = [1] x2 + [8]         
            p(False) = [0]                  
                p(S) = [1]                  
             p(True) = [2]                  
                p(Z) = [1]                  
             p(add0) = [2] x2 + [2]         
             p(goal) = [4] x1 + [1]         
           p(isZero) = [1]                  
             p(mul0) = [4]                  
           p(second) = [0]                  
            p(add0#) = [1]                  
            p(goal#) = [1] x1 + [8] x2 + [1]
          p(isZero#) = [1]                  
            p(mul0#) = [2] x1 + [8] x2 + [0]
          p(second#) = [1] x1 + [0]         
              p(c_1) = [8] x1 + [1]         
              p(c_2) = [1]                  
              p(c_3) = [1]                  
              p(c_4) = [1]                  
              p(c_5) = [2]                  
              p(c_6) = [1] x1 + [8]         
              p(c_7) = [1]                  
              p(c_8) = [1]                  
        
        Following rules are strictly oriented:
        mul0#(C(x,y),y') = [2] y + [8] y' + [16]
                         > [2] y + [8] y' + [8] 
                         = c_6(mul0#(y,y'))     
        
        
        Following rules are (at-least) weakly oriented:
        
*** Step 1.b:6.a:4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            mul0#(C(x,y),y') -> c_6(mul0#(y,y'))
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 1.b:6.b:1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
        - Weak DPs:
            mul0#(C(x,y),y') -> add0#(mul0(y,y'),y')
            mul0#(C(x,y),y') -> mul0#(y,y')
        - Weak TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/2,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + 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(c_1) = {1}
        
        Following symbols are considered usable:
          {add0,mul0,add0#,goal#,isZero#,mul0#,second#}
        TcT has computed the following interpretation:
                p(C) = 2 + x2                                 
            p(False) = 1                                      
                p(S) = 0                                      
             p(True) = 0                                      
                p(Z) = 2                                      
             p(add0) = 1 + x1 + x2                            
             p(goal) = 1 + 2*x1 + x1*x2 + 4*x2 + x2^2         
           p(isZero) = 4 + 2*x1 + 4*x1^2                      
             p(mul0) = x1*x2 + 2*x1^2 + 3*x2 + x2^2           
           p(second) = 1 + 2*x1 + x1^2                        
            p(add0#) = x1                                     
            p(goal#) = 1 + 2*x1 + 4*x1*x2 + x1^2 + x2 + 2*x2^2
          p(isZero#) = 4 + x1^2                               
            p(mul0#) = 4 + x1 + 4*x1*x2 + 2*x1^2 + 4*x2^2     
          p(second#) = 1 + x1 + 4*x1^2                        
              p(c_1) = x1                                     
              p(c_2) = 4                                      
              p(c_3) = 1                                      
              p(c_4) = 0                                      
              p(c_5) = 0                                      
              p(c_6) = 1 + x1 + x2                            
              p(c_7) = 0                                      
              p(c_8) = 0                                      
        
        Following rules are strictly oriented:
        add0#(C(x,y),y') = 2 + y                  
                         > y                      
                         = c_1(add0#(y,C(S(),y')))
        
        
        Following rules are (at-least) weakly oriented:
        mul0#(C(x,y),y') =  14 + 9*y + 4*y*y' + 2*y^2 + 8*y' + 4*y'^2
                         >= y*y' + 2*y^2 + 3*y' + y'^2               
                         =  add0#(mul0(y,y'),y')                     
        
        mul0#(C(x,y),y') =  14 + 9*y + 4*y*y' + 2*y^2 + 8*y' + 4*y'^2
                         >= 4 + y + 4*y*y' + 2*y^2 + 4*y'^2          
                         =  mul0#(y,y')                              
        
         add0(C(x,y),y') =  3 + y + y'                               
                         >= 3 + y + y'                               
                         =  add0(y,C(S(),y'))                        
        
             add0(Z(),y) =  3 + y                                    
                         >= y                                        
                         =  y                                        
        
         mul0(C(x,y),y') =  8 + 8*y + y*y' + 2*y^2 + 5*y' + y'^2     
                         >= 1 + y*y' + 2*y^2 + 4*y' + y'^2           
                         =  add0(mul0(y,y'),y')                      
        
             mul0(Z(),y) =  8 + 5*y + y^2                            
                         >= 2                                        
                         =  Z()                                      
        
*** Step 1.b:6.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y')))
            mul0#(C(x,y),y') -> add0#(mul0(y,y'),y')
            mul0#(C(x,y),y') -> mul0#(y,y')
        - Weak TRS:
            add0(C(x,y),y') -> add0(y,C(S(),y'))
            add0(Z(),y) -> y
            mul0(C(x,y),y') -> add0(mul0(y,y'),y')
            mul0(Z(),y) -> Z()
        - Signature:
            {add0/2,goal/2,isZero/1,mul0/2,second/1,add0#/2,goal#/2,isZero#/1,mul0#/2,second#/1} / {C/2,False/0,S/0
            ,True/0,Z/0,c_1/1,c_2/0,c_3/1,c_4/0,c_5/0,c_6/2,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add0#,goal#,isZero#,mul0#,second#} and constructors {C
            ,False,S,True,Z}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^3))