MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y) -> nil()
            if(true(),x,y) -> cons(x,int(s(x),y))
            int(x,y) -> if(le(x,y),x,y)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/3,int/2,le/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if,int,le} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          if#(false(),x,y) -> c_1()
          if#(true(),x,y) -> c_2(int#(s(x),y))
          int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y))
          le#(0(),y) -> c_4()
          le#(s(x),0()) -> c_5()
          le#(s(x),s(y)) -> c_6(le#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y) -> c_1()
            if#(true(),x,y) -> c_2(int#(s(x),y))
            int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y))
            le#(0(),y) -> c_4()
            le#(s(x),0()) -> c_5()
            le#(s(x),s(y)) -> c_6(le#(x,y))
        - Weak TRS:
            if(false(),x,y) -> nil()
            if(true(),x,y) -> cons(x,int(s(x),y))
            int(x,y) -> if(le(x,y),x,y)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/3,int/2,le/2,if#/3,int#/2,le#/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0
            ,c_6/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,int#,le#} and constructors {0,cons,false,nil,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) -> c_1()
          if#(true(),x,y) -> c_2(int#(s(x),y))
          int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y))
          le#(0(),y) -> c_4()
          le#(s(x),0()) -> c_5()
          le#(s(x),s(y)) -> c_6(le#(x,y))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,y) -> c_1()
            if#(true(),x,y) -> c_2(int#(s(x),y))
            int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y))
            le#(0(),y) -> c_4()
            le#(s(x),0()) -> c_5()
            le#(s(x),s(y)) -> c_6(le#(x,y))
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/3,int/2,le/2,if#/3,int#/2,le#/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0
            ,c_6/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,int#,le#} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,5}
        by application of
          Pre({1,4,5}) = {3,6}.
        Here rules are labelled as follows:
          1: if#(false(),x,y) -> c_1()
          2: if#(true(),x,y) -> c_2(int#(s(x),y))
          3: int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y))
          4: le#(0(),y) -> c_4()
          5: le#(s(x),0()) -> c_5()
          6: le#(s(x),s(y)) -> c_6(le#(x,y))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(true(),x,y) -> c_2(int#(s(x),y))
            int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y))
            le#(s(x),s(y)) -> c_6(le#(x,y))
        - Weak DPs:
            if#(false(),x,y) -> c_1()
            le#(0(),y) -> c_4()
            le#(s(x),0()) -> c_5()
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/3,int/2,le/2,if#/3,int#/2,le#/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0
            ,c_6/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,int#,le#} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:if#(true(),x,y) -> c_2(int#(s(x),y))
             -->_1 int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y)):2
          
          2:S:int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y))
             -->_2 le#(s(x),s(y)) -> c_6(le#(x,y)):3
             -->_2 le#(s(x),0()) -> c_5():6
             -->_2 le#(0(),y) -> c_4():5
             -->_1 if#(false(),x,y) -> c_1():4
             -->_1 if#(true(),x,y) -> c_2(int#(s(x),y)):1
          
          3:S:le#(s(x),s(y)) -> c_6(le#(x,y))
             -->_1 le#(s(x),0()) -> c_5():6
             -->_1 le#(0(),y) -> c_4():5
             -->_1 le#(s(x),s(y)) -> c_6(le#(x,y)):3
          
          4:W:if#(false(),x,y) -> c_1()
             
          
          5:W:le#(0(),y) -> c_4()
             
          
          6:W:le#(s(x),0()) -> c_5()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: if#(false(),x,y) -> c_1()
          5: le#(0(),y) -> c_4()
          6: le#(s(x),0()) -> c_5()
* Step 5: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(true(),x,y) -> c_2(int#(s(x),y))
            int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y))
            le#(s(x),s(y)) -> c_6(le#(x,y))
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
        - Signature:
            {if/3,int/2,le/2,if#/3,int#/2,le#/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0
            ,c_6/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,int#,le#} and constructors {0,cons,false,nil,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(c_2) = {1},
            uargs(c_3) = {1,2},
            uargs(c_6) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [2]                  
             p(cons) = [1]                  
            p(false) = [2]                  
               p(if) = [0]                  
              p(int) = [0]                  
               p(le) = [2]                  
              p(nil) = [0]                  
                p(s) = [0]                  
             p(true) = [1]                  
              p(if#) = [1] x1 + [2]         
             p(int#) = [15]                 
              p(le#) = [9]                  
              p(c_1) = [0]                  
              p(c_2) = [1] x1 + [0]         
              p(c_3) = [1] x1 + [1] x2 + [1]
              p(c_4) = [0]                  
              p(c_5) = [1]                  
              p(c_6) = [1] x1 + [5]         
          
          Following rules are strictly oriented:
          int#(x,y) = [15]                          
                    > [14]                          
                    = c_3(if#(le(x,y),x,y),le#(x,y))
          
          
          Following rules are (at-least) weakly oriented:
          if#(true(),x,y) =  [3]              
                          >= [15]             
                          =  c_2(int#(s(x),y))
          
           le#(s(x),s(y)) =  [9]              
                          >= [14]             
                          =  c_6(le#(x,y))    
          
                le(0(),y) =  [2]              
                          >= [1]              
                          =  true()           
          
             le(s(x),0()) =  [2]              
                          >= [2]              
                          =  false()          
          
            le(s(x),s(y)) =  [2]              
                          >= [2]              
                          =  le(x,y)          
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          if#(true(),x,y) -> c_2(int#(s(x),y))
          le#(s(x),s(y)) -> c_6(le#(x,y))
      - Weak DPs:
          int#(x,y) -> c_3(if#(le(x,y),x,y),le#(x,y))
      - Weak TRS:
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
      - Signature:
          {if/3,int/2,le/2,if#/3,int#/2,le#/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0,c_1/0,c_2/1,c_3/2,c_4/0,c_5/0
          ,c_6/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {if#,int#,le#} and constructors {0,cons,false,nil,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE