MAYBE

Problem:
 cond1(true(),x,y) -> cond2(gr(x,y),x,y)
 cond2(true(),x,y) -> cond1(neq(x,0()),y,y)
 cond2(false(),x,y) -> cond1(neq(x,0()),p(x),y)
 gr(0(),x) -> false()
 gr(s(x),0()) -> true()
 gr(s(x),s(y)) -> gr(x,y)
 neq(0(),0()) -> false()
 neq(0(),s(x)) -> true()
 neq(s(x),0()) -> true()
 neq(s(x),s(y)) -> neq(x,y)
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   cond1#(true(),x,y) -> gr#(x,y)
   cond1#(true(),x,y) -> cond2#(gr(x,y),x,y)
   cond2#(true(),x,y) -> neq#(x,0())
   cond2#(true(),x,y) -> cond1#(neq(x,0()),y,y)
   cond2#(false(),x,y) -> p#(x)
   cond2#(false(),x,y) -> neq#(x,0())
   cond2#(false(),x,y) -> cond1#(neq(x,0()),p(x),y)
   gr#(s(x),s(y)) -> gr#(x,y)
   neq#(s(x),s(y)) -> neq#(x,y)
  TRS:
   cond1(true(),x,y) -> cond2(gr(x,y),x,y)
   cond2(true(),x,y) -> cond1(neq(x,0()),y,y)
   cond2(false(),x,y) -> cond1(neq(x,0()),p(x),y)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y)) -> gr(x,y)
   neq(0(),0()) -> false()
   neq(0(),s(x)) -> true()
   neq(s(x),0()) -> true()
   neq(s(x),s(y)) -> neq(x,y)
   p(0()) -> 0()
   p(s(x)) -> x
  Open