YES

Problem:
 active(and(tt(),X)) -> mark(X)
 active(plus(N,0())) -> mark(N)
 active(plus(N,s(M))) -> mark(s(plus(N,M)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(tt()) -> active(tt())
 mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
 mark(0()) -> active(0())
 mark(s(X)) -> active(s(mark(X)))
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 and(active(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 plus(mark(X1),X2) -> plus(X1,X2)
 plus(X1,mark(X2)) -> plus(X1,X2)
 plus(active(X1),X2) -> plus(X1,X2)
 plus(X1,active(X2)) -> plus(X1,X2)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 0 1]  
   [s](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                    [1 0 1]     [1 0 1]  
   [plus](x0, x1) = [1 0 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 0]  ,
   
         [1]
   [0] = [0]
         [0],
   
                [1 0 1]  
   [mark](x0) = [0 0 0]x0
                [0 0 0]  ,
   
                  [1 0 0]  
   [active](x0) = [0 0 0]x0
                  [0 0 1]  ,
   
                   [1 0 1]     [1 0 1]  
   [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  ,
   
          [1]
   [tt] = [0]
          [0]
  orientation:
                         [1 0 1]    [1]    [1 0 1]           
   active(and(tt(),X)) = [0 0 0]X + [0] >= [0 0 0]X = mark(X)
                         [0 0 0]    [0]    [0 0 0]           
   
                         [1 0 1]    [1]    [1 0 1]           
   active(plus(N,0())) = [0 0 0]N + [0] >= [0 0 0]N = mark(N)
                         [0 0 0]    [0]    [0 0 0]           
   
                          [1 0 1]    [1 0 1]     [1 0 1]    [1 0 1]                      
   active(plus(N,s(M))) = [0 0 0]M + [0 0 0]N >= [0 0 0]M + [0 0 0]N = mark(s(plus(N,M)))
                          [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]                      
   
                      [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]                             
   mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(and(mark(X1),X2))
                      [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                             
   
                [1]    [1]               
   mark(tt()) = [0] >= [0] = active(tt())
                [0]    [0]               
   
                       [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]                                    
   mark(plus(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(plus(mark(X1),mark(X2)))
                       [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                                    
   
               [1]    [1]              
   mark(0()) = [0] >= [0] = active(0())
               [0]    [0]              
   
                [1 0 1]     [1 0 1]                      
   mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X)))
                [0 0 0]     [0 0 0]                      
   
                      [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]               
   and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2)
                      [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]               
   
                      [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]               
   and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2)
                      [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]               
   
                        [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]               
   and(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2)
                        [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]               
   
                        [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]               
   and(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2)
                        [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]               
   
                       [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]                
   plus(mark(X1),X2) = [1 0 1]X1 + [0 0 0]X2 >= [1 0 0]X1 + [0 0 0]X2 = plus(X1,X2)
                       [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                
   
                       [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]                
   plus(X1,mark(X2)) = [1 0 0]X1 + [0 0 0]X2 >= [1 0 0]X1 + [0 0 0]X2 = plus(X1,X2)
                       [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                
   
                         [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]                
   plus(active(X1),X2) = [1 0 0]X1 + [0 0 0]X2 >= [1 0 0]X1 + [0 0 0]X2 = plus(X1,X2)
                         [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                
   
                         [1 0 1]     [1 0 1]      [1 0 1]     [1 0 1]                
   plus(X1,active(X2)) = [1 0 0]X1 + [0 0 0]X2 >= [1 0 0]X1 + [0 0 0]X2 = plus(X1,X2)
                         [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                
   
                [1 0 1]     [1 0 1]        
   s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X)
                [0 0 0]     [0 0 0]        
   
                  [1 0 1]     [1 0 1]        
   s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X)
                  [0 0 0]     [0 0 0]        
  problem:
   active(plus(N,s(M))) -> mark(s(plus(N,M)))
   mark(and(X1,X2)) -> active(and(mark(X1),X2))
   mark(tt()) -> active(tt())
   mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
   mark(0()) -> active(0())
   mark(s(X)) -> active(s(mark(X)))
   and(mark(X1),X2) -> and(X1,X2)
   and(X1,mark(X2)) -> and(X1,X2)
   and(active(X1),X2) -> and(X1,X2)
   and(X1,active(X2)) -> and(X1,X2)
   plus(mark(X1),X2) -> plus(X1,X2)
   plus(X1,mark(X2)) -> plus(X1,X2)
   plus(active(X1),X2) -> plus(X1,X2)
   plus(X1,active(X2)) -> plus(X1,X2)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [s](x0) = x0 + 1,
    
    [plus](x0, x1) = 4x0 + 2x1,
    
    [0] = 0,
    
    [mark](x0) = x0,
    
    [active](x0) = x0,
    
    [and](x0, x1) = 4x0 + x1,
    
    [tt] = 4
   orientation:
    active(plus(N,s(M))) = 2M + 4N + 2 >= 2M + 4N + 1 = mark(s(plus(N,M)))
    
    mark(and(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = active(and(mark(X1),X2))
    
    mark(tt()) = 4 >= 4 = active(tt())
    
    mark(plus(X1,X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = active(plus(mark(X1),mark(X2)))
    
    mark(0()) = 0 >= 0 = active(0())
    
    mark(s(X)) = X + 1 >= X + 1 = active(s(mark(X)))
    
    and(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = and(X1,X2)
    
    and(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = and(X1,X2)
    
    and(active(X1),X2) = 4X1 + X2 >= 4X1 + X2 = and(X1,X2)
    
    and(X1,active(X2)) = 4X1 + X2 >= 4X1 + X2 = and(X1,X2)
    
    plus(mark(X1),X2) = 4X1 + 2X2 >= 4X1 + 2X2 = plus(X1,X2)
    
    plus(X1,mark(X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = plus(X1,X2)
    
    plus(active(X1),X2) = 4X1 + 2X2 >= 4X1 + 2X2 = plus(X1,X2)
    
    plus(X1,active(X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = plus(X1,X2)
    
    s(mark(X)) = X + 1 >= X + 1 = s(X)
    
    s(active(X)) = X + 1 >= X + 1 = s(X)
   problem:
    mark(and(X1,X2)) -> active(and(mark(X1),X2))
    mark(tt()) -> active(tt())
    mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
    mark(0()) -> active(0())
    mark(s(X)) -> active(s(mark(X)))
    and(mark(X1),X2) -> and(X1,X2)
    and(X1,mark(X2)) -> and(X1,X2)
    and(active(X1),X2) -> and(X1,X2)
    and(X1,active(X2)) -> and(X1,X2)
    plus(mark(X1),X2) -> plus(X1,X2)
    plus(X1,mark(X2)) -> plus(X1,X2)
    plus(active(X1),X2) -> plus(X1,X2)
    plus(X1,active(X2)) -> plus(X1,X2)
    s(mark(X)) -> s(X)
    s(active(X)) -> s(X)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [s](x0) = 2x0 + 3,
     
     [plus](x0, x1) = 4x0 + 2x1 + 3,
     
     [0] = 4,
     
     [mark](x0) = 3x0,
     
     [active](x0) = x0 + 6,
     
     [and](x0, x1) = x0 + x1 + 3,
     
     [tt] = 7
    orientation:
     mark(and(X1,X2)) = 3X1 + 3X2 + 9 >= 3X1 + X2 + 9 = active(and(mark(X1),X2))
     
     mark(tt()) = 21 >= 13 = active(tt())
     
     mark(plus(X1,X2)) = 12X1 + 6X2 + 9 >= 12X1 + 6X2 + 9 = active(plus(mark(X1),mark(X2)))
     
     mark(0()) = 12 >= 10 = active(0())
     
     mark(s(X)) = 6X + 9 >= 6X + 9 = active(s(mark(X)))
     
     and(mark(X1),X2) = 3X1 + X2 + 3 >= X1 + X2 + 3 = and(X1,X2)
     
     and(X1,mark(X2)) = X1 + 3X2 + 3 >= X1 + X2 + 3 = and(X1,X2)
     
     and(active(X1),X2) = X1 + X2 + 9 >= X1 + X2 + 3 = and(X1,X2)
     
     and(X1,active(X2)) = X1 + X2 + 9 >= X1 + X2 + 3 = and(X1,X2)
     
     plus(mark(X1),X2) = 12X1 + 2X2 + 3 >= 4X1 + 2X2 + 3 = plus(X1,X2)
     
     plus(X1,mark(X2)) = 4X1 + 6X2 + 3 >= 4X1 + 2X2 + 3 = plus(X1,X2)
     
     plus(active(X1),X2) = 4X1 + 2X2 + 27 >= 4X1 + 2X2 + 3 = plus(X1,X2)
     
     plus(X1,active(X2)) = 4X1 + 2X2 + 15 >= 4X1 + 2X2 + 3 = plus(X1,X2)
     
     s(mark(X)) = 6X + 3 >= 2X + 3 = s(X)
     
     s(active(X)) = 2X + 15 >= 2X + 3 = s(X)
    problem:
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
     mark(s(X)) -> active(s(mark(X)))
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     plus(mark(X1),X2) -> plus(X1,X2)
     plus(X1,mark(X2)) -> plus(X1,X2)
     s(mark(X)) -> s(X)
    DP Processor:
     DPs:
      mark#(and(X1,X2)) -> mark#(X1)
      mark#(and(X1,X2)) -> and#(mark(X1),X2)
      mark#(plus(X1,X2)) -> mark#(X2)
      mark#(plus(X1,X2)) -> mark#(X1)
      mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2))
      mark#(s(X)) -> mark#(X)
      mark#(s(X)) -> s#(mark(X))
      and#(mark(X1),X2) -> and#(X1,X2)
      and#(X1,mark(X2)) -> and#(X1,X2)
      plus#(mark(X1),X2) -> plus#(X1,X2)
      plus#(X1,mark(X2)) -> plus#(X1,X2)
      s#(mark(X)) -> s#(X)
     TRS:
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
      mark(s(X)) -> active(s(mark(X)))
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      plus(mark(X1),X2) -> plus(X1,X2)
      plus(X1,mark(X2)) -> plus(X1,X2)
      s(mark(X)) -> s(X)
     TDG Processor:
      DPs:
       mark#(and(X1,X2)) -> mark#(X1)
       mark#(and(X1,X2)) -> and#(mark(X1),X2)
       mark#(plus(X1,X2)) -> mark#(X2)
       mark#(plus(X1,X2)) -> mark#(X1)
       mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2))
       mark#(s(X)) -> mark#(X)
       mark#(s(X)) -> s#(mark(X))
       and#(mark(X1),X2) -> and#(X1,X2)
       and#(X1,mark(X2)) -> and#(X1,X2)
       plus#(mark(X1),X2) -> plus#(X1,X2)
       plus#(X1,mark(X2)) -> plus#(X1,X2)
       s#(mark(X)) -> s#(X)
      TRS:
       mark(and(X1,X2)) -> active(and(mark(X1),X2))
       mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
       mark(s(X)) -> active(s(mark(X)))
       and(mark(X1),X2) -> and(X1,X2)
       and(X1,mark(X2)) -> and(X1,X2)
       plus(mark(X1),X2) -> plus(X1,X2)
       plus(X1,mark(X2)) -> plus(X1,X2)
       s(mark(X)) -> s(X)
      graph:
       s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
       plus#(mark(X1),X2) -> plus#(X1,X2) ->
       plus#(X1,mark(X2)) -> plus#(X1,X2)
       plus#(mark(X1),X2) -> plus#(X1,X2) ->
       plus#(mark(X1),X2) -> plus#(X1,X2)
       plus#(X1,mark(X2)) -> plus#(X1,X2) ->
       plus#(X1,mark(X2)) -> plus#(X1,X2)
       plus#(X1,mark(X2)) -> plus#(X1,X2) ->
       plus#(mark(X1),X2) -> plus#(X1,X2)
       and#(mark(X1),X2) -> and#(X1,X2) ->
       and#(X1,mark(X2)) -> and#(X1,X2)
       and#(mark(X1),X2) -> and#(X1,X2) ->
       and#(mark(X1),X2) -> and#(X1,X2)
       and#(X1,mark(X2)) -> and#(X1,X2) ->
       and#(X1,mark(X2)) -> and#(X1,X2)
       and#(X1,mark(X2)) -> and#(X1,X2) ->
       and#(mark(X1),X2) -> and#(X1,X2)
       mark#(s(X)) -> s#(mark(X)) -> s#(mark(X)) -> s#(X)
       mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X))
       mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
       mark#(s(X)) -> mark#(X) ->
       mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2))
       mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1)
       mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2)
       mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2)
       mark#(s(X)) -> mark#(X) ->
       mark#(and(X1,X2)) -> mark#(X1)
       mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) ->
       plus#(X1,mark(X2)) -> plus#(X1,X2)
       mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) ->
       plus#(mark(X1),X2) -> plus#(X1,X2)
       mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> s#(mark(X))
       mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
       mark#(plus(X1,X2)) -> mark#(X2) ->
       mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2))
       mark#(plus(X1,X2)) -> mark#(X2) ->
       mark#(plus(X1,X2)) -> mark#(X1)
       mark#(plus(X1,X2)) -> mark#(X2) ->
       mark#(plus(X1,X2)) -> mark#(X2)
       mark#(plus(X1,X2)) -> mark#(X2) ->
       mark#(and(X1,X2)) -> and#(mark(X1),X2)
       mark#(plus(X1,X2)) -> mark#(X2) ->
       mark#(and(X1,X2)) -> mark#(X1)
       mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X))
       mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
       mark#(plus(X1,X2)) -> mark#(X1) ->
       mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2))
       mark#(plus(X1,X2)) -> mark#(X1) ->
       mark#(plus(X1,X2)) -> mark#(X1)
       mark#(plus(X1,X2)) -> mark#(X1) ->
       mark#(plus(X1,X2)) -> mark#(X2)
       mark#(plus(X1,X2)) -> mark#(X1) ->
       mark#(and(X1,X2)) -> and#(mark(X1),X2)
       mark#(plus(X1,X2)) -> mark#(X1) ->
       mark#(and(X1,X2)) -> mark#(X1)
       mark#(and(X1,X2)) -> and#(mark(X1),X2) ->
       and#(X1,mark(X2)) -> and#(X1,X2)
       mark#(and(X1,X2)) -> and#(mark(X1),X2) ->
       and#(mark(X1),X2) -> and#(X1,X2)
       mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X))
       mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
       mark#(and(X1,X2)) -> mark#(X1) ->
       mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2))
       mark#(and(X1,X2)) -> mark#(X1) ->
       mark#(plus(X1,X2)) -> mark#(X1)
       mark#(and(X1,X2)) -> mark#(X1) ->
       mark#(plus(X1,X2)) -> mark#(X2)
       mark#(and(X1,X2)) -> mark#(X1) ->
       mark#(and(X1,X2)) -> and#(mark(X1),X2)
       mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1)
      SCC Processor:
       #sccs: 4
       #rules: 9
       #arcs: 42/144
       DPs:
        mark#(s(X)) -> mark#(X)
        mark#(and(X1,X2)) -> mark#(X1)
        mark#(plus(X1,X2)) -> mark#(X2)
        mark#(plus(X1,X2)) -> mark#(X1)
       TRS:
        mark(and(X1,X2)) -> active(and(mark(X1),X2))
        mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
        mark(s(X)) -> active(s(mark(X)))
        and(mark(X1),X2) -> and(X1,X2)
        and(X1,mark(X2)) -> and(X1,X2)
        plus(mark(X1),X2) -> plus(X1,X2)
        plus(X1,mark(X2)) -> plus(X1,X2)
        s(mark(X)) -> s(X)
       Subterm Criterion Processor:
        simple projection:
         pi(mark#) = 0
        problem:
         DPs:
          
         TRS:
          mark(and(X1,X2)) -> active(and(mark(X1),X2))
          mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
          mark(s(X)) -> active(s(mark(X)))
          and(mark(X1),X2) -> and(X1,X2)
          and(X1,mark(X2)) -> and(X1,X2)
          plus(mark(X1),X2) -> plus(X1,X2)
          plus(X1,mark(X2)) -> plus(X1,X2)
          s(mark(X)) -> s(X)
        Qed
       
       DPs:
        and#(mark(X1),X2) -> and#(X1,X2)
        and#(X1,mark(X2)) -> and#(X1,X2)
       TRS:
        mark(and(X1,X2)) -> active(and(mark(X1),X2))
        mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
        mark(s(X)) -> active(s(mark(X)))
        and(mark(X1),X2) -> and(X1,X2)
        and(X1,mark(X2)) -> and(X1,X2)
        plus(mark(X1),X2) -> plus(X1,X2)
        plus(X1,mark(X2)) -> plus(X1,X2)
        s(mark(X)) -> s(X)
       Subterm Criterion Processor:
        simple projection:
         pi(and#) = 1
        problem:
         DPs:
          and#(mark(X1),X2) -> and#(X1,X2)
         TRS:
          mark(and(X1,X2)) -> active(and(mark(X1),X2))
          mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
          mark(s(X)) -> active(s(mark(X)))
          and(mark(X1),X2) -> and(X1,X2)
          and(X1,mark(X2)) -> and(X1,X2)
          plus(mark(X1),X2) -> plus(X1,X2)
          plus(X1,mark(X2)) -> plus(X1,X2)
          s(mark(X)) -> s(X)
        Subterm Criterion Processor:
         simple projection:
          pi(and#) = 0
         problem:
          DPs:
           
          TRS:
           mark(and(X1,X2)) -> active(and(mark(X1),X2))
           mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
           mark(s(X)) -> active(s(mark(X)))
           and(mark(X1),X2) -> and(X1,X2)
           and(X1,mark(X2)) -> and(X1,X2)
           plus(mark(X1),X2) -> plus(X1,X2)
           plus(X1,mark(X2)) -> plus(X1,X2)
           s(mark(X)) -> s(X)
         Qed
       
       DPs:
        plus#(mark(X1),X2) -> plus#(X1,X2)
        plus#(X1,mark(X2)) -> plus#(X1,X2)
       TRS:
        mark(and(X1,X2)) -> active(and(mark(X1),X2))
        mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
        mark(s(X)) -> active(s(mark(X)))
        and(mark(X1),X2) -> and(X1,X2)
        and(X1,mark(X2)) -> and(X1,X2)
        plus(mark(X1),X2) -> plus(X1,X2)
        plus(X1,mark(X2)) -> plus(X1,X2)
        s(mark(X)) -> s(X)
       Subterm Criterion Processor:
        simple projection:
         pi(plus#) = 1
        problem:
         DPs:
          plus#(mark(X1),X2) -> plus#(X1,X2)
         TRS:
          mark(and(X1,X2)) -> active(and(mark(X1),X2))
          mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
          mark(s(X)) -> active(s(mark(X)))
          and(mark(X1),X2) -> and(X1,X2)
          and(X1,mark(X2)) -> and(X1,X2)
          plus(mark(X1),X2) -> plus(X1,X2)
          plus(X1,mark(X2)) -> plus(X1,X2)
          s(mark(X)) -> s(X)
        Subterm Criterion Processor:
         simple projection:
          pi(plus#) = 0
         problem:
          DPs:
           
          TRS:
           mark(and(X1,X2)) -> active(and(mark(X1),X2))
           mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
           mark(s(X)) -> active(s(mark(X)))
           and(mark(X1),X2) -> and(X1,X2)
           and(X1,mark(X2)) -> and(X1,X2)
           plus(mark(X1),X2) -> plus(X1,X2)
           plus(X1,mark(X2)) -> plus(X1,X2)
           s(mark(X)) -> s(X)
         Qed
       
       DPs:
        s#(mark(X)) -> s#(X)
       TRS:
        mark(and(X1,X2)) -> active(and(mark(X1),X2))
        mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
        mark(s(X)) -> active(s(mark(X)))
        and(mark(X1),X2) -> and(X1,X2)
        and(X1,mark(X2)) -> and(X1,X2)
        plus(mark(X1),X2) -> plus(X1,X2)
        plus(X1,mark(X2)) -> plus(X1,X2)
        s(mark(X)) -> s(X)
       Subterm Criterion Processor:
        simple projection:
         pi(s#) = 0
        problem:
         DPs:
          
         TRS:
          mark(and(X1,X2)) -> active(and(mark(X1),X2))
          mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
          mark(s(X)) -> active(s(mark(X)))
          and(mark(X1),X2) -> and(X1,X2)
          and(X1,mark(X2)) -> and(X1,X2)
          plus(mark(X1),X2) -> plus(X1,X2)
          plus(X1,mark(X2)) -> plus(X1,X2)
          s(mark(X)) -> s(X)
        Qed