MAYBE
* Step 1: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            cond(true(),x,y) -> cond(gr(x,y),p(x),s(y))
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond/3,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond,gr,p} and constructors {0,false,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(cond) = {1,2}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [0]                           
             p(cond) = [1] x1 + [1] x2 + [3] x3 + [4]
            p(false) = [0]                           
               p(gr) = [8]                           
                p(p) = [1] x1 + [0]                  
                p(s) = [1] x1 + [0]                  
             p(true) = [0]                           
          
          Following rules are strictly oriented:
             gr(0(),x) = [8]    
                       > [0]    
                       = false()
          
          gr(s(x),0()) = [8]    
                       > [0]    
                       = true() 
          
          
          Following rules are (at-least) weakly oriented:
          cond(true(),x,y) =  [1] x + [3] y + [4]    
                           >= [1] x + [3] y + [12]   
                           =  cond(gr(x,y),p(x),s(y))
          
             gr(s(x),s(y)) =  [8]                    
                           >= [8]                    
                           =  gr(x,y)                
          
                    p(0()) =  [0]                    
                           >= [0]                    
                           =  0()                    
          
                   p(s(x)) =  [1] x + [0]            
                           >= [1] x + [0]            
                           =  x                      
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: NaturalMI MAYBE
    + Considered Problem:
        - Strict TRS:
            cond(true(),x,y) -> cond(gr(x,y),p(x),s(y))
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Weak TRS:
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
        - Signature:
            {cond/3,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond,gr,p} and constructors {0,false,s,true}
    + 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(cond) = {1,2}
        
        Following symbols are considered usable:
          {cond,gr,p}
        TcT has computed the following interpretation:
              p(0) = [2]                  
           p(cond) = [8] x1 + [4] x2 + [0]
          p(false) = [0]                  
             p(gr) = [0]                  
              p(p) = [1] x1 + [0]         
              p(s) = [1] x1 + [4]         
           p(true) = [0]                  
        
        Following rules are strictly oriented:
        p(s(x)) = [1] x + [4]
                > [1] x + [0]
                = x          
        
        
        Following rules are (at-least) weakly oriented:
        cond(true(),x,y) =  [4] x + [0]            
                         >= [4] x + [0]            
                         =  cond(gr(x,y),p(x),s(y))
        
               gr(0(),x) =  [0]                    
                         >= [0]                    
                         =  false()                
        
            gr(s(x),0()) =  [0]                    
                         >= [0]                    
                         =  true()                 
        
           gr(s(x),s(y)) =  [0]                    
                         >= [0]                    
                         =  gr(x,y)                
        
                  p(0()) =  [2]                    
                         >= [2]                    
                         =  0()                    
        
* Step 3: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            cond(true(),x,y) -> cond(gr(x,y),p(x),s(y))
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
        - Weak TRS:
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            p(s(x)) -> x
        - Signature:
            {cond/3,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond,gr,p} and constructors {0,false,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(cond) = {1,2}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [10]                  
             p(cond) = [1] x1 + [1] x2 + [13]
            p(false) = [0]                   
               p(gr) = [0]                   
                p(p) = [1] x1 + [8]          
                p(s) = [1] x1 + [8]          
             p(true) = [0]                   
          
          Following rules are strictly oriented:
          p(0()) = [18]
                 > [10]
                 = 0() 
          
          
          Following rules are (at-least) weakly oriented:
          cond(true(),x,y) =  [1] x + [13]           
                           >= [1] x + [21]           
                           =  cond(gr(x,y),p(x),s(y))
          
                 gr(0(),x) =  [0]                    
                           >= [0]                    
                           =  false()                
          
              gr(s(x),0()) =  [0]                    
                           >= [0]                    
                           =  true()                 
          
             gr(s(x),s(y)) =  [0]                    
                           >= [0]                    
                           =  gr(x,y)                
          
                   p(s(x)) =  [1] x + [16]           
                           >= [1] x + [0]            
                           =  x                      
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          cond(true(),x,y) -> cond(gr(x,y),p(x),s(y))
          gr(s(x),s(y)) -> gr(x,y)
      - Weak TRS:
          gr(0(),x) -> false()
          gr(s(x),0()) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
      - Signature:
          {cond/3,gr/2,p/1} / {0/0,false/0,s/1,true/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {cond,gr,p} and constructors {0,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE