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())
  TDG 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#(s(x),s(0())) -> evenodd#(x,0())
    evenodd#(s(x),s(0())) -> evenodd#(x,0()) ->
    evenodd#(x,0()) -> not#(evenodd(x,s(0())))
    evenodd#(s(x),s(0())) -> evenodd#(x,0()) ->
    evenodd#(x,0()) -> evenodd#(x,s(0()))
    evenodd#(x,0()) -> evenodd#(x,s(0())) ->
    evenodd#(s(x),s(0())) -> evenodd#(x,0())
    evenodd#(x,0()) -> evenodd#(x,s(0())) ->
    evenodd#(x,0()) -> not#(evenodd(x,s(0())))
    evenodd#(x,0()) -> evenodd#(x,s(0())) -> evenodd#(x,0()) -> evenodd#(x,s(0()))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    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())
     EDG Processor:
      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())
      graph:
       
      Qed