MAYBE
* Step 1: WeightGap 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:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(cons) = {2},
            uargs(if) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [0]                  
             p(cons) = [1] x1 + [1] x2 + [0]
            p(false) = [0]                  
               p(if) = [1] x1 + [2] x2 + [0]
              p(int) = [8] x1 + [0]         
               p(le) = [0]                  
              p(nil) = [0]                  
                p(s) = [0]                  
             p(true) = [1]                  
          
          Following rules are strictly oriented:
          if(true(),x,y) = [2] x + [1]        
                         > [1] x + [0]        
                         = cons(x,int(s(x),y))
          
          
          Following rules are (at-least) weakly oriented:
          if(false(),x,y) =  [2] x + [0]    
                          >= [0]            
                          =  nil()          
          
                 int(x,y) =  [8] x + [0]    
                          >= [2] x + [0]    
                          =  if(le(x,y),x,y)
          
                le(0(),y) =  [0]            
                          >= [1]            
                          =  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 2: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            if(false(),x,y) -> nil()
            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)
        - Weak TRS:
            if(true(),x,y) -> cons(x,int(s(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:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(cons) = {2},
            uargs(if) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [0]                  
             p(cons) = [1] x1 + [1] x2 + [0]
            p(false) = [1]                  
               p(if) = [1] x1 + [2] x2 + [0]
              p(int) = [8] x1 + [0]         
               p(le) = [0]                  
              p(nil) = [0]                  
                p(s) = [0]                  
             p(true) = [0]                  
          
          Following rules are strictly oriented:
          if(false(),x,y) = [2] x + [1]
                          > [0]        
                          = nil()      
          
          
          Following rules are (at-least) weakly oriented:
          if(true(),x,y) =  [2] x + [0]        
                         >= [1] x + [0]        
                         =  cons(x,int(s(x),y))
          
                int(x,y) =  [8] x + [0]        
                         >= [2] x + [0]        
                         =  if(le(x,y),x,y)    
          
               le(0(),y) =  [0]                
                         >= [0]                
                         =  true()             
          
            le(s(x),0()) =  [0]                
                         >= [1]                
                         =  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 3: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            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)
        - Weak TRS:
            if(false(),x,y) -> nil()
            if(true(),x,y) -> cons(x,int(s(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:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(cons) = {2},
            uargs(if) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [0]                  
             p(cons) = [1] x1 + [1] x2 + [0]
            p(false) = [1]                  
               p(if) = [1] x1 + [8] x2 + [6]
              p(int) = [10] x1 + [12]       
               p(le) = [2]                  
              p(nil) = [0]                  
                p(s) = [0]                  
             p(true) = [6]                  
          
          Following rules are strictly oriented:
              int(x,y) = [10] x + [12]  
                       > [8] x + [8]    
                       = if(le(x,y),x,y)
          
          le(s(x),0()) = [2]            
                       > [1]            
                       = false()        
          
          
          Following rules are (at-least) weakly oriented:
          if(false(),x,y) =  [8] x + [7]        
                          >= [0]                
                          =  nil()              
          
           if(true(),x,y) =  [8] x + [12]       
                          >= [1] x + [12]       
                          =  cons(x,int(s(x),y))
          
                le(0(),y) =  [2]                
                          >= [6]                
                          =  true()             
          
            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 4: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          le(0(),y) -> true()
          le(s(x),s(y)) -> 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(s(x),0()) -> false()
      - 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:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE