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())
  EDG 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())
   graph:
    evenodd#(s(x),s(0())) -> evenodd#(x,0()) ->
    evenodd#(x,0()) -> evenodd#(x,s(0()))
    evenodd#(s(x),s(0())) -> evenodd#(x,0()) ->
    evenodd#(x,0()) -> not#(evenodd(x,s(0())))
    evenodd#(x,0()) -> evenodd#(x,s(0())) -> evenodd#(s(x),s(0())) -> evenodd#(x,0())
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 3/9
    DPs:
     evenodd#(s(x),s(0())) -> evenodd#(x,0())
     evenodd#(x,0()) -> evenodd#(x,s(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())
    Subterm Criterion Processor:
     simple projection:
      pi(evenodd#) = 0
     problem:
      DPs:
       evenodd#(x,0()) -> evenodd#(x,s(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:
      dimension: 1
      interpretation:
       [evenodd#](x0, x1) = x1,
       
       [s](x0) = 0,
       
       [evenodd](x0, x1) = 1,
       
       [0] = 1,
       
       [false] = 1,
       
       [not](x0) = x0,
       
       [true] = 1
      orientation:
       evenodd#(x,0()) = 1 >= 0 = evenodd#(x,s(0()))
       
       not(true()) = 1 >= 1 = false()
       
       not(false()) = 1 >= 1 = true()
       
       evenodd(x,0()) = 1 >= 1 = not(evenodd(x,s(0())))
       
       evenodd(0(),s(0())) = 1 >= 1 = false()
       
       evenodd(s(x),s(0())) = 1 >= 1 = evenodd(x,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