YES

Problem:
 not(true()) -> false()
 not(false()) -> true()
 evenodd(x,0()) -> not(evenodd(x,s(0())))
 evenodd(0(),s(0())) -> false()
 evenodd(s(x),s(0())) -> evenodd(x,0())

Proof:
 DP Processor:
  DPs:
   evenodd#(x,0()) -> evenodd#(x,s(0()))
   evenodd#(x,0()) -> not#(evenodd(x,s(0())))
   evenodd#(s(x),s(0())) -> evenodd#(x,0())
  TRS:
   not(true()) -> false()
   not(false()) -> true()
   evenodd(x,0()) -> not(evenodd(x,s(0())))
   evenodd(0(),s(0())) -> false()
   evenodd(s(x),s(0())) -> evenodd(x,0())
  Matrix Interpretation Processor: dim=4
   
   usable rules:
    
   interpretation:
    [evenodd#](x0, x1) = [1 1 1 0]x0 + [0 0 1 0]x1,
    
    [not#](x0) = [0],
    
              [0 0 1 1]     [1]
              [0 1 1 0]     [1]
    [s](x0) = [1 0 0 1]x0 + [0]
              [1 1 1 0]     [0],
    
                        [0 0 1 1]     [0 0 0 0]     [1]
                        [0 0 1 1]     [0 0 0 0]     [0]
    [evenodd](x0, x1) = [1 0 0 1]x0 + [1 0 0 0]x1 + [0]
                        [0 0 0 0]     [0 0 0 0]     [0],
    
          [0]
          [1]
    [0] = [1]
          [0],
    
              [1]
              [0]
    [false] = [1]
              [1],
    
                [1 0 1 0]  
                [1 1 0 1]  
    [not](x0) = [0 1 0 1]x0
                [0 0 1 1]  ,
    
             [1]
             [1]
    [true] = [1]
             [1]
   orientation:
    evenodd#(x,0()) = [1 1 1 0]x + [1] >= [1 1 1 0]x = evenodd#(x,s(0()))
    
    evenodd#(x,0()) = [1 1 1 0]x + [1] >= [0] = not#(evenodd(x,s(0())))
    
    evenodd#(s(x),s(0())) = [1 1 2 2]x + [2] >= [1 1 1 0]x + [1] = evenodd#(x,0())
    
                  [2]    [1]          
                  [3]    [0]          
    not(true()) = [2] >= [1] = false()
                  [2]    [1]          
    
                   [2]    [1]         
                   [2]    [1]         
    not(false()) = [1] >= [1] = true()
                   [2]    [1]         
    
                     [0 0 1 1]    [1]    [1 0 1 2]    [3]                         
                     [0 0 1 1]    [0]    [0 0 2 2]    [1]                         
    evenodd(x,0()) = [1 0 0 1]x + [0] >= [0 0 1 1]x + [0] = not(evenodd(x,s(0())))
                     [0 0 0 0]    [0]    [1 0 0 1]    [2]                         
    
                          [2]    [1]          
                          [1]    [0]          
    evenodd(0(),s(0())) = [2] >= [1] = false()
                          [0]    [1]          
    
                           [2 1 1 1]    [1]    [0 0 1 1]    [1]                 
                           [2 1 1 1]    [0]    [0 0 1 1]    [0]                 
    evenodd(s(x),s(0())) = [1 1 2 1]x + [3] >= [1 0 0 1]x + [0] = evenodd(x,0())
                           [0 0 0 0]    [0]    [0 0 0 0]    [0]                 
   problem:
    DPs:
     
    TRS:
     not(true()) -> false()
     not(false()) -> true()
     evenodd(x,0()) -> not(evenodd(x,s(0())))
     evenodd(0(),s(0())) -> false()
     evenodd(s(x),s(0())) -> evenodd(x,0())
   Qed