MAYBE
* Step 1: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            cond(true(),x,y) -> cond(gr(x,y),p(x),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) = [4]                            
             p(cond) = [1] x1 + [1] x2 + [11] x3 + [0]
            p(false) = [2]                            
               p(gr) = [10]                           
                p(p) = [1] x1 + [3]                   
                p(s) = [1] x1 + [0]                   
             p(true) = [0]                            
          
          Following rules are strictly oriented:
             gr(0(),x) = [10]       
                       > [2]        
                       = false()    
          
          gr(s(x),0()) = [10]       
                       > [0]        
                       = true()     
          
                p(0()) = [7]        
                       > [4]        
                       = 0()        
          
               p(s(x)) = [1] x + [3]
                       > [1] x + [0]
                       = x          
          
          
          Following rules are (at-least) weakly oriented:
          cond(true(),x,y) =  [1] x + [11] y + [0] 
                           >= [1] x + [11] y + [13]
                           =  cond(gr(x,y),p(x),y) 
          
             gr(s(x),s(y)) =  [10]                 
                           >= [10]                 
                           =  gr(x,y)              
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          cond(true(),x,y) -> cond(gr(x,y),p(x),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