MAYBE

Problem:
 cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
 and(x,false()) -> false()
 and(false(),x) -> false()
 and(true(),true()) -> true()
 even(0()) -> true()
 even(s(0())) -> false()
 even(s(s(x))) -> even(x)
 gr(0(),x) -> false()
 gr(s(x),0()) -> true()
 gr(s(x),s(y())) -> gr(x,y())
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   cond#(true(),x) -> p#(x)
   cond#(true(),x) -> gr#(x,0())
   cond#(true(),x) -> even#(x)
   cond#(true(),x) -> and#(even(x),gr(x,0()))
   cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
   even#(s(s(x))) -> even#(x)
   gr#(s(x),s(y())) -> gr#(x,y())
  TRS:
   cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
   and(x,false()) -> false()
   and(false(),x) -> false()
   and(true(),true()) -> true()
   even(0()) -> true()
   even(s(0())) -> false()
   even(s(s(x))) -> even(x)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y())) -> gr(x,y())
   p(0()) -> 0()
   p(s(x)) -> x
  Usable Rule Processor:
   DPs:
    cond#(true(),x) -> p#(x)
    cond#(true(),x) -> gr#(x,0())
    cond#(true(),x) -> even#(x)
    cond#(true(),x) -> and#(even(x),gr(x,0()))
    cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
    even#(s(s(x))) -> even#(x)
    gr#(s(x),s(y())) -> gr#(x,y())
   TRS:
    f15(x,y) -> x
    f15(x,y) -> y
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    even(0()) -> true()
    even(s(0())) -> false()
    even(s(s(x))) -> even(x)
    p(0()) -> 0()
    p(s(x)) -> x
    and(x,false()) -> false()
    and(false(),x) -> false()
    and(true(),true()) -> true()
   EDG Processor:
    DPs:
     cond#(true(),x) -> p#(x)
     cond#(true(),x) -> gr#(x,0())
     cond#(true(),x) -> even#(x)
     cond#(true(),x) -> and#(even(x),gr(x,0()))
     cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
     even#(s(s(x))) -> even#(x)
     gr#(s(x),s(y())) -> gr#(x,y())
    TRS:
     f15(x,y) -> x
     f15(x,y) -> y
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     even(0()) -> true()
     even(s(0())) -> false()
     even(s(s(x))) -> even(x)
     p(0()) -> 0()
     p(s(x)) -> x
     and(x,false()) -> false()
     and(false(),x) -> false()
     and(true(),true()) -> true()
    graph:
     even#(s(s(x))) -> even#(x) -> even#(s(s(x))) -> even#(x)
     cond#(true(),x) -> even#(x) ->
     even#(s(s(x))) -> even#(x)
     cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
     cond#(true(),x) -> p#(x)
     cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
     cond#(true(),x) -> gr#(x,0())
     cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
     cond#(true(),x) -> even#(x)
     cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
     cond#(true(),x) -> and#(even(x),gr(x,0()))
     cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x)) ->
     cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
    Restore Modifier:
     DPs:
      cond#(true(),x) -> p#(x)
      cond#(true(),x) -> gr#(x,0())
      cond#(true(),x) -> even#(x)
      cond#(true(),x) -> and#(even(x),gr(x,0()))
      cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
      even#(s(s(x))) -> even#(x)
      gr#(s(x),s(y())) -> gr#(x,y())
     TRS:
      cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
      and(x,false()) -> false()
      and(false(),x) -> false()
      and(true(),true()) -> true()
      even(0()) -> true()
      even(s(0())) -> false()
      even(s(s(x))) -> even(x)
      gr(0(),x) -> false()
      gr(s(x),0()) -> true()
      gr(s(x),s(y())) -> gr(x,y())
      p(0()) -> 0()
      p(s(x)) -> x
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 7/49
      DPs:
       cond#(true(),x) -> cond#(and(even(x),gr(x,0())),p(x))
      TRS:
       cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
       and(x,false()) -> false()
       and(false(),x) -> false()
       and(true(),true()) -> true()
       even(0()) -> true()
       even(s(0())) -> false()
       even(s(s(x))) -> even(x)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y())) -> gr(x,y())
       p(0()) -> 0()
       p(s(x)) -> x
      Open
      
      DPs:
       even#(s(s(x))) -> even#(x)
      TRS:
       cond(true(),x) -> cond(and(even(x),gr(x,0())),p(x))
       and(x,false()) -> false()
       and(false(),x) -> false()
       and(true(),true()) -> true()
       even(0()) -> true()
       even(s(0())) -> false()
       even(s(s(x))) -> even(x)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y())) -> gr(x,y())
       p(0()) -> 0()
       p(s(x)) -> x
      Open