YES

Problem:
 active(f(0())) -> mark(cons(0(),f(s(0()))))
 active(f(s(0()))) -> mark(f(p(s(0()))))
 active(p(s(X))) -> mark(X)
 mark(f(X)) -> active(f(mark(X)))
 mark(0()) -> active(0())
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(s(X)) -> active(s(mark(X)))
 mark(p(X)) -> active(p(mark(X)))
 f(mark(X)) -> f(X)
 f(active(X)) -> f(X)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons(active(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)
 p(mark(X)) -> p(X)
 p(active(X)) -> p(X)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 1 0]  
   [p](x0) = [0 0 0]x0
             [1 1 0]  ,
   
                [1 1 0]  
   [mark](x0) = [0 0 0]x0
                [0 0 1]  ,
   
                    [1 1 0]     [1 0 0]  
   [cons](x0, x1) = [0 0 1]x0 + [0 0 1]x1
                    [0 0 0]     [1 0 0]  ,
   
             [1 1 0]     [0]
   [s](x0) = [0 0 1]x0 + [0]
             [0 0 0]     [1],
   
                  [1 1 0]  
   [active](x0) = [0 0 0]x0
                  [0 0 1]  ,
   
             [1 1 0]  
   [f](x0) = [0 0 1]x0
             [0 0 0]  ,
   
         [0]
   [0] = [0]
         [0]
  orientation:
                    [0]    [0]                            
   active(f(0())) = [0] >= [0] = mark(cons(0(),f(s(0()))))
                    [0]    [0]                            
   
                       [1]    [0]                     
   active(f(s(0()))) = [0] >= [0] = mark(f(p(s(0()))))
                       [0]    [0]                     
   
                     [1 1 1]     [1 1 0]           
   active(p(s(X))) = [0 0 0]X >= [0 0 0]X = mark(X)
                     [1 1 1]     [0 0 1]           
   
                [1 1 1]     [1 1 1]                      
   mark(f(X)) = [0 0 0]X >= [0 0 0]X = active(f(mark(X)))
                [0 0 0]     [0 0 0]                      
   
               [0]    [0]              
   mark(0()) = [0] >= [0] = active(0())
               [0]    [0]              
   
                       [1 1 1]     [1 0 1]      [1 1 1]     [1 0 1]                              
   mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2))
                       [0 0 0]     [1 0 0]      [0 0 0]     [1 0 0]                              
   
                [1 1 1]    [0]    [1 1 1]    [0]                     
   mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(s(mark(X)))
                [0 0 0]    [1]    [0 0 0]    [1]                     
   
                [1 1 0]     [1 1 0]                      
   mark(p(X)) = [0 0 0]X >= [0 0 0]X = active(p(mark(X)))
                [1 1 0]     [1 1 0]                      
   
                [1 1 0]     [1 1 0]        
   f(mark(X)) = [0 0 1]X >= [0 0 1]X = f(X)
                [0 0 0]     [0 0 0]        
   
                  [1 1 0]     [1 1 0]        
   f(active(X)) = [0 0 1]X >= [0 0 1]X = f(X)
                  [0 0 0]     [0 0 0]        
   
                       [1 1 0]     [1 0 0]      [1 1 0]     [1 0 0]                
   cons(mark(X1),X2) = [0 0 1]X1 + [0 0 1]X2 >= [0 0 1]X1 + [0 0 1]X2 = cons(X1,X2)
                       [0 0 0]     [1 0 0]      [0 0 0]     [1 0 0]                
   
                       [1 1 0]     [1 1 0]      [1 1 0]     [1 0 0]                
   cons(X1,mark(X2)) = [0 0 1]X1 + [0 0 1]X2 >= [0 0 1]X1 + [0 0 1]X2 = cons(X1,X2)
                       [0 0 0]     [1 1 0]      [0 0 0]     [1 0 0]                
   
                         [1 1 0]     [1 0 0]      [1 1 0]     [1 0 0]                
   cons(active(X1),X2) = [0 0 1]X1 + [0 0 1]X2 >= [0 0 1]X1 + [0 0 1]X2 = cons(X1,X2)
                         [0 0 0]     [1 0 0]      [0 0 0]     [1 0 0]                
   
                         [1 1 0]     [1 1 0]      [1 1 0]     [1 0 0]                
   cons(X1,active(X2)) = [0 0 1]X1 + [0 0 1]X2 >= [0 0 1]X1 + [0 0 1]X2 = cons(X1,X2)
                         [0 0 0]     [1 1 0]      [0 0 0]     [1 0 0]                
   
                [1 1 0]    [0]    [1 1 0]    [0]       
   s(mark(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = s(X)
                [0 0 0]    [1]    [0 0 0]    [1]       
   
                  [1 1 0]    [0]    [1 1 0]    [0]       
   s(active(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = s(X)
                  [0 0 0]    [1]    [0 0 0]    [1]       
   
                [1 1 0]     [1 1 0]        
   p(mark(X)) = [0 0 0]X >= [0 0 0]X = p(X)
                [1 1 0]     [1 1 0]        
   
                  [1 1 0]     [1 1 0]        
   p(active(X)) = [0 0 0]X >= [0 0 0]X = p(X)
                  [1 1 0]     [1 1 0]        
  problem:
   active(f(0())) -> mark(cons(0(),f(s(0()))))
   active(p(s(X))) -> mark(X)
   mark(f(X)) -> active(f(mark(X)))
   mark(0()) -> active(0())
   mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
   mark(s(X)) -> active(s(mark(X)))
   mark(p(X)) -> active(p(mark(X)))
   f(mark(X)) -> f(X)
   f(active(X)) -> f(X)
   cons(mark(X1),X2) -> cons(X1,X2)
   cons(X1,mark(X2)) -> cons(X1,X2)
   cons(active(X1),X2) -> cons(X1,X2)
   cons(X1,active(X2)) -> cons(X1,X2)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
   p(mark(X)) -> p(X)
   p(active(X)) -> p(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 1 1]     [1]
    [p](x0) = [1 0 0]x0 + [0]
              [0 0 0]     [0],
    
                 [1 0 0]  
    [mark](x0) = [0 0 0]x0
                 [0 1 1]  ,
    
                     [1 1 1]     [1 1 1]  
    [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 0 0]  ,
    
              [1 1 1]  
    [s](x0) = [0 0 0]x0
              [0 0 0]  ,
    
                   [1 0 0]  
    [active](x0) = [0 0 1]x0
                   [0 1 0]  ,
    
              [1 0 0]  
    [f](x0) = [0 0 0]x0
              [0 0 0]  ,
    
          [0]
    [0] = [0]
          [0]
   orientation:
                     [0]    [0]                            
    active(f(0())) = [0] >= [0] = mark(cons(0(),f(s(0()))))
                     [0]    [0]                            
    
                      [1 1 1]    [1]    [1 0 0]           
    active(p(s(X))) = [0 0 0]X + [0] >= [0 0 0]X = mark(X)
                      [1 1 1]    [0]    [0 1 1]           
    
                 [1 0 0]     [1 0 0]                      
    mark(f(X)) = [0 0 0]X >= [0 0 0]X = active(f(mark(X)))
                 [0 0 0]     [0 0 0]                      
    
                [0]    [0]              
    mark(0()) = [0] >= [0] = active(0())
                [0]    [0]              
    
                        [1 1 1]     [1 1 1]      [1 1 1]     [1 1 1]                              
    mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2))
                        [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                              
    
                 [1 1 1]     [1 1 1]                      
    mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X)))
                 [0 0 0]     [0 0 0]                      
    
                 [1 1 1]    [1]    [1 1 1]    [1]                     
    mark(p(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(p(mark(X)))
                 [1 0 0]    [0]    [1 0 0]    [0]                     
    
                 [1 0 0]     [1 0 0]        
    f(mark(X)) = [0 0 0]X >= [0 0 0]X = f(X)
                 [0 0 0]     [0 0 0]        
    
                   [1 0 0]     [1 0 0]        
    f(active(X)) = [0 0 0]X >= [0 0 0]X = f(X)
                   [0 0 0]     [0 0 0]        
    
                        [1 1 1]     [1 1 1]      [1 1 1]     [1 1 1]                
    cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2)
                        [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                
    
                        [1 1 1]     [1 1 1]      [1 1 1]     [1 1 1]                
    cons(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2)
                        [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                
    
                          [1 1 1]     [1 1 1]      [1 1 1]     [1 1 1]                
    cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2)
                          [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                
    
                          [1 1 1]     [1 1 1]      [1 1 1]     [1 1 1]                
    cons(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2)
                          [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                
    
                 [1 1 1]     [1 1 1]        
    s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X)
                 [0 0 0]     [0 0 0]        
    
                   [1 1 1]     [1 1 1]        
    s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X)
                   [0 0 0]     [0 0 0]        
    
                 [1 1 1]    [1]    [1 1 1]    [1]       
    p(mark(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = p(X)
                 [0 0 0]    [0]    [0 0 0]    [0]       
    
                   [1 1 1]    [1]    [1 1 1]    [1]       
    p(active(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = p(X)
                   [0 0 0]    [0]    [0 0 0]    [0]       
   problem:
    active(f(0())) -> mark(cons(0(),f(s(0()))))
    mark(f(X)) -> active(f(mark(X)))
    mark(0()) -> active(0())
    mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    mark(s(X)) -> active(s(mark(X)))
    mark(p(X)) -> active(p(mark(X)))
    f(mark(X)) -> f(X)
    f(active(X)) -> f(X)
    cons(mark(X1),X2) -> cons(X1,X2)
    cons(X1,mark(X2)) -> cons(X1,X2)
    cons(active(X1),X2) -> cons(X1,X2)
    cons(X1,active(X2)) -> cons(X1,X2)
    s(mark(X)) -> s(X)
    s(active(X)) -> s(X)
    p(mark(X)) -> p(X)
    p(active(X)) -> p(X)
   Bounds Processor:
    bound: 3
    enrichment: match
    automaton:
     final states: {20,19,18,17,15,13,11,10,6,1}
     transitions:
      p1(5) -> 16*
      p1(22) -> 16*
      p1(12) -> 16*
      p1(7) -> 16*
      p1(2) -> 16*
      p1(14) -> 16*
      p1(9) -> 16*
      p1(36) -> 16*
      p1(16) -> 16*
      p1(38) -> 16*
      p1(28) -> 16*
      s1(25) -> 26*
      s1(5) -> 14*
      s1(22) -> 14*
      s1(12) -> 14*
      s1(7) -> 14*
      s1(2) -> 14*
      s1(14) -> 14*
      s1(9) -> 14*
      s1(36) -> 14*
      s1(16) -> 14*
      s1(38) -> 14*
      s1(28) -> 14*
      cons1(38,7) -> 12*
      cons1(28,7) -> 12*
      cons1(5,7) -> 12*
      cons1(25,27) -> 28*
      cons1(22,7) -> 12*
      cons1(12,7) -> 12*
      cons1(7,7) -> 12*
      cons1(2,7) -> 12*
      cons1(14,7) -> 12*
      cons1(9,7) -> 12*
      cons1(35,4) -> 36*
      cons1(25,4) -> 22*
      cons1(36,7) -> 12*
      cons1(16,7) -> 12*
      cons1(2,4) -> 22*
      f1(5) -> 9*
      f1(22) -> 9*
      f1(12) -> 9*
      f1(7) -> 9*
      f1(2) -> 9*
      f1(14) -> 9*
      f1(9) -> 9*
      f1(36) -> 9*
      f1(26) -> 27*
      f1(16) -> 9*
      f1(38) -> 9*
      f1(28) -> 9*
      active1(25) -> 35,21
      active1(36) -> 1,6,8
      mark1(2) -> 35*
      mark1(28) -> 6,8
      01() -> 25*
      cons2(37,27) -> 38*
      cons2(25,4) -> 36*
      cons2(2,4) -> 36*
      active2(42) -> 37*
      active2(38) -> 6*
      f70() -> 7*
      mark2(25) -> 37*
      mark0(5) -> 1*
      mark0(7) -> 8*
      mark0(2) -> 21*
      cons3(25,27) -> 38*
      cons3(42,27) -> 38*
      cons0(8,7) -> 12*
      cons0(5,7) -> 12*
      cons0(21,4) -> 22*
      cons0(22,7) -> 12*
      cons0(12,7) -> 12*
      cons0(7,7) -> 12,18
      cons0(2,7) -> 12*
      cons0(14,7) -> 12*
      cons0(9,7) -> 12*
      cons0(16,7) -> 12*
      cons0(2,4) -> 22,5
      02() -> 42*
      00() -> 2*
      f0(5) -> 9*
      f0(22) -> 9*
      f0(12) -> 9*
      f0(7) -> 9,17
      f0(2) -> 9*
      f0(14) -> 9*
      f0(9) -> 9*
      f0(16) -> 9*
      f0(8) -> 9*
      f0(3) -> 4*
      s0(5) -> 14*
      s0(22) -> 14*
      s0(12) -> 14*
      s0(7) -> 14,19
      s0(2) -> 14,3
      s0(14) -> 14*
      s0(9) -> 14*
      s0(16) -> 14*
      s0(8) -> 14*
      active0(22) -> 1*
      active0(12) -> 11*
      active0(2) -> 21,10
      active0(14) -> 13*
      active0(9) -> 6*
      active0(16) -> 15*
      p0(5) -> 16*
      p0(22) -> 16*
      p0(12) -> 16*
      p0(7) -> 16,20
      p0(2) -> 16*
      p0(14) -> 16*
      p0(9) -> 16*
      p0(16) -> 16*
      p0(8) -> 16*
      1 -> 6*
      6 -> 8*
      10 -> 8*
      11 -> 8*
      13 -> 8*
      15 -> 8*
    problem:
     
    Qed