MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y,z,u,v) -> if2(le(y,s(u)),x,y,s(z),s(u),v)
            if(true(),x,y,z,u,v) -> v
            if2(false(),x,y,z,u,v) -> quotIter(x,y,z,u,v)
            if2(true(),x,y,z,u,v) -> quotIter(x,y,z,0(),s(v))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            quot(x,0()) -> quotZeroErro()
            quot(x,s(y)) -> quotIter(x,s(y),0(),0(),0())
            quotIter(x,s(y),z,u,v) -> if(le(x,z),x,s(y),z,u,v)
        - Signature:
            {if/6,if2/6,le/2,quot/2,quotIter/5} / {0/0,false/0,quotZeroErro/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if,if2,le,quot,quotIter} and constructors {0,false
            ,quotZeroErro,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
          if#(true(),x,y,z,u,v) -> c_2()
          if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
          if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
          le#(0(),y) -> c_5()
          le#(s(x),0()) -> c_6()
          le#(s(x),s(y)) -> c_7(le#(x,y))
          quot#(x,0()) -> c_8()
          quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0()))
          quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
            if#(true(),x,y,z,u,v) -> c_2()
            if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
            if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
            le#(0(),y) -> c_5()
            le#(s(x),0()) -> c_6()
            le#(s(x),s(y)) -> c_7(le#(x,y))
            quot#(x,0()) -> c_8()
            quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0()))
            quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
        - Weak TRS:
            if(false(),x,y,z,u,v) -> if2(le(y,s(u)),x,y,s(z),s(u),v)
            if(true(),x,y,z,u,v) -> v
            if2(false(),x,y,z,u,v) -> quotIter(x,y,z,u,v)
            if2(true(),x,y,z,u,v) -> quotIter(x,y,z,0(),s(v))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            quot(x,0()) -> quotZeroErro()
            quot(x,s(y)) -> quotIter(x,s(y),0(),0(),0())
            quotIter(x,s(y),z,u,v) -> if(le(x,z),x,s(y),z,u,v)
        - Signature:
            {if/6,if2/6,le/2,quot/2,quotIter/5,if#/6,if2#/6,le#/2,quot#/2,quotIter#/5} / {0/0,false/0,quotZeroErro/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,if2#,le#,quot#,quotIter#} and constructors {0,false
            ,quotZeroErro,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
          if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
          if#(true(),x,y,z,u,v) -> c_2()
          if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
          if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
          le#(0(),y) -> c_5()
          le#(s(x),0()) -> c_6()
          le#(s(x),s(y)) -> c_7(le#(x,y))
          quot#(x,0()) -> c_8()
          quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0()))
          quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
            if#(true(),x,y,z,u,v) -> c_2()
            if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
            if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
            le#(0(),y) -> c_5()
            le#(s(x),0()) -> c_6()
            le#(s(x),s(y)) -> c_7(le#(x,y))
            quot#(x,0()) -> c_8()
            quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0()))
            quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/6,if2/6,le/2,quot/2,quotIter/5,if#/6,if2#/6,le#/2,quot#/2,quotIter#/5} / {0/0,false/0,quotZeroErro/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,if2#,le#,quot#,quotIter#} and constructors {0,false
            ,quotZeroErro,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,5,6,8}
        by application of
          Pre({2,5,6,8}) = {1,7,10}.
        Here rules are labelled as follows:
          1: if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
          2: if#(true(),x,y,z,u,v) -> c_2()
          3: if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
          4: if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
          5: le#(0(),y) -> c_5()
          6: le#(s(x),0()) -> c_6()
          7: le#(s(x),s(y)) -> c_7(le#(x,y))
          8: quot#(x,0()) -> c_8()
          9: quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0()))
          10: quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
            if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
            if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
            le#(s(x),s(y)) -> c_7(le#(x,y))
            quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0()))
            quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
        - Weak DPs:
            if#(true(),x,y,z,u,v) -> c_2()
            le#(0(),y) -> c_5()
            le#(s(x),0()) -> c_6()
            quot#(x,0()) -> c_8()
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/6,if2/6,le/2,quot/2,quotIter/5,if#/6,if2#/6,le#/2,quot#/2,quotIter#/5} / {0/0,false/0,quotZeroErro/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,if2#,le#,quot#,quotIter#} and constructors {0,false
            ,quotZeroErro,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
             -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):4
             -->_1 if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v))):3
             -->_1 if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v)):2
             -->_2 le#(0(),y) -> c_5():8
          
          2:S:if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
             -->_1 quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z)):6
          
          3:S:if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
             -->_1 quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z)):6
          
          4:S:le#(s(x),s(y)) -> c_7(le#(x,y))
             -->_1 le#(s(x),0()) -> c_6():9
             -->_1 le#(0(),y) -> c_5():8
             -->_1 le#(s(x),s(y)) -> c_7(le#(x,y)):4
          
          5:S:quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0()))
             -->_1 quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z)):6
          
          6:S:quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
             -->_2 le#(s(x),0()) -> c_6():9
             -->_2 le#(0(),y) -> c_5():8
             -->_1 if#(true(),x,y,z,u,v) -> c_2():7
             -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):4
             -->_1 if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u))):1
          
          7:W:if#(true(),x,y,z,u,v) -> c_2()
             
          
          8:W:le#(0(),y) -> c_5()
             
          
          9:W:le#(s(x),0()) -> c_6()
             
          
          10:W:quot#(x,0()) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          10: quot#(x,0()) -> c_8()
          7: if#(true(),x,y,z,u,v) -> c_2()
          8: le#(0(),y) -> c_5()
          9: le#(s(x),0()) -> c_6()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
            if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
            if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
            le#(s(x),s(y)) -> c_7(le#(x,y))
            quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0()))
            quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/6,if2/6,le/2,quot/2,quotIter/5,if#/6,if2#/6,le#/2,quot#/2,quotIter#/5} / {0/0,false/0,quotZeroErro/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,if2#,le#,quot#,quotIter#} and constructors {0,false
            ,quotZeroErro,s,true}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
           -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):4
           -->_1 if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v))):3
           -->_1 if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v)):2
        
        2:S:if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
           -->_1 quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z)):6
        
        3:S:if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
           -->_1 quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z)):6
        
        4:S:le#(s(x),s(y)) -> c_7(le#(x,y))
           -->_1 le#(s(x),s(y)) -> c_7(le#(x,y)):4
        
        5:S:quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0()))
           -->_1 quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z)):6
        
        6:S:quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
           -->_2 le#(s(x),s(y)) -> c_7(le#(x,y)):4
           -->_1 if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u))):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).
        
        [(5,quot#(x,s(y)) -> c_9(quotIter#(x,s(y),0(),0(),0())))]
* Step 6: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
            if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
            if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
            le#(s(x),s(y)) -> c_7(le#(x,y))
            quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/6,if2/6,le/2,quot/2,quotIter/5,if#/6,if2#/6,le#/2,quot#/2,quotIter#/5} / {0/0,false/0,quotZeroErro/0,s/1
            ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,if2#,le#,quot#,quotIter#} and constructors {0,false
            ,quotZeroErro,s,true}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            uargs(if#) = {1},
            uargs(if2#) = {1},
            uargs(c_1) = {1,2},
            uargs(c_3) = {1},
            uargs(c_4) = {1},
            uargs(c_7) = {1},
            uargs(c_10) = {1,2}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                       p(0) = [2]                                             
                   p(false) = [0]                                             
                      p(if) = [0]                                             
                     p(if2) = [0]                                             
                      p(le) = [0]                                             
                    p(quot) = [0]                                             
                p(quotIter) = [0]                                             
            p(quotZeroErro) = [0]                                             
                       p(s) = [0]                                             
                    p(true) = [0]                                             
                     p(if#) = [1] x1 + [2] x2 + [4] x3 + [2] x6 + [2]         
                    p(if2#) = [1] x1 + [2] x2 + [2] x3 + [1] x5 + [2] x6 + [0]
                     p(le#) = [0]                                             
                   p(quot#) = [2]                                             
               p(quotIter#) = [2] x1 + [1] x4 + [2] x5 + [3]                  
                     p(c_1) = [1] x1 + [1] x2 + [0]                           
                     p(c_2) = [0]                                             
                     p(c_3) = [1] x1 + [0]                                    
                     p(c_4) = [1] x1 + [0]                                    
                     p(c_5) = [0]                                             
                     p(c_6) = [0]                                             
                     p(c_7) = [1] x1 + [0]                                    
                     p(c_8) = [0]                                             
                     p(c_9) = [0]                                             
                    p(c_10) = [1] x1 + [1] x2 + [0]                           
          
          Following rules are strictly oriented:
           if#(false(),x,y,z,u,v) = [2] v + [2] x + [4] y + [2]                      
                                  > [2] v + [2] x + [2] y + [0]                      
                                  = c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
          
          quotIter#(x,s(y),z,u,v) = [1] u + [2] v + [2] x + [3]                      
                                  > [2] v + [2] x + [2]                              
                                  = c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))         
          
          
          Following rules are (at-least) weakly oriented:
          if2#(false(),x,y,z,u,v) =  [1] u + [2] v + [2] x + [2] y + [0]
                                  >= [1] u + [2] v + [2] x + [3]        
                                  =  c_3(quotIter#(x,y,z,u,v))          
          
           if2#(true(),x,y,z,u,v) =  [1] u + [2] v + [2] x + [2] y + [0]
                                  >= [2] x + [5]                        
                                  =  c_4(quotIter#(x,y,z,0(),s(v)))     
          
                   le#(s(x),s(y)) =  [0]                                
                                  >= [0]                                
                                  =  c_7(le#(x,y))                      
          
                        le(0(),y) =  [0]                                
                                  >= [0]                                
                                  =  true()                             
          
                     le(s(x),0()) =  [0]                                
                                  >= [0]                                
                                  =  false()                            
          
                    le(s(x),s(y)) =  [0]                                
                                  >= [0]                                
                                  =  le(x,y)                            
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 7: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          if2#(false(),x,y,z,u,v) -> c_3(quotIter#(x,y,z,u,v))
          if2#(true(),x,y,z,u,v) -> c_4(quotIter#(x,y,z,0(),s(v)))
          le#(s(x),s(y)) -> c_7(le#(x,y))
      - Weak DPs:
          if#(false(),x,y,z,u,v) -> c_1(if2#(le(y,s(u)),x,y,s(z),s(u),v),le#(y,s(u)))
          quotIter#(x,s(y),z,u,v) -> c_10(if#(le(x,z),x,s(y),z,u,v),le#(x,z))
      - Weak TRS:
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
      - Signature:
          {if/6,if2/6,le/2,quot/2,quotIter/5,if#/6,if2#/6,le#/2,quot#/2,quotIter#/5} / {0/0,false/0,quotZeroErro/0,s/1
          ,true/0,c_1/2,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1,c_10/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {if#,if2#,le#,quot#,quotIter#} and constructors {0,false
          ,quotZeroErro,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE