MAYBE
* Step 1: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            f(true(),x,y) -> f(gt(x,y),s(x),s(s(y)))
            gt(0(),v) -> false()
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Signature:
            {f/3,gt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,gt} 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(f) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [0]                  
                p(f) = [1] x1 + [2] x3 + [3]
            p(false) = [0]                  
               p(gt) = [1]                  
                p(s) = [8]                  
             p(true) = [1]                  
          
          Following rules are strictly oriented:
          gt(0(),v) = [1]    
                    > [0]    
                    = false()
          
          
          Following rules are (at-least) weakly oriented:
          f(true(),x,y) =  [2] y + [4]            
                        >= [20]                   
                        =  f(gt(x,y),s(x),s(s(y)))
          
           gt(s(u),0()) =  [1]                    
                        >= [1]                    
                        =  true()                 
          
          gt(s(u),s(v)) =  [1]                    
                        >= [1]                    
                        =  gt(u,v)                
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: WeightGap MAYBE
    + Considered Problem:
        - Strict TRS:
            f(true(),x,y) -> f(gt(x,y),s(x),s(s(y)))
            gt(s(u),0()) -> true()
            gt(s(u),s(v)) -> gt(u,v)
        - Weak TRS:
            gt(0(),v) -> false()
        - Signature:
            {f/3,gt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,gt} 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(f) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [8]                           
                p(f) = [1] x1 + [1] x2 + [2] x3 + [0]
            p(false) = [1]                           
               p(gt) = [10]                          
                p(s) = [0]                           
             p(true) = [0]                           
          
          Following rules are strictly oriented:
          gt(s(u),0()) = [10]  
                       > [0]   
                       = true()
          
          
          Following rules are (at-least) weakly oriented:
          f(true(),x,y) =  [1] x + [2] y + [0]    
                        >= [10]                   
                        =  f(gt(x,y),s(x),s(s(y)))
          
              gt(0(),v) =  [10]                   
                        >= [1]                    
                        =  false()                
          
          gt(s(u),s(v)) =  [10]                   
                        >= [10]                   
                        =  gt(u,v)                
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 3: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          f(true(),x,y) -> f(gt(x,y),s(x),s(s(y)))
          gt(s(u),s(v)) -> gt(u,v)
      - Weak TRS:
          gt(0(),v) -> false()
          gt(s(u),0()) -> true()
      - Signature:
          {f/3,gt/2} / {0/0,false/0,s/1,true/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {f,gt} and constructors {0,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE