MAYBE

Problem:
 cond1(true(),x,y) -> cond2(gr(x,0()),x,y)
 cond2(true(),x,y) -> cond1(gr(add(x,y),0()),p(x),y)
 cond2(false(),x,y) -> cond3(gr(y,0()),x,y)
 cond3(true(),x,y) -> cond1(gr(add(x,y),0()),x,p(y))
 cond3(false(),x,y) -> cond1(gr(add(x,y),0()),x,y)
 gr(0(),x) -> false()
 gr(s(x),0()) -> true()
 gr(s(x),s(y)) -> gr(x,y)
 add(0(),x) -> x
 add(s(x),y) -> s(add(x,y))
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   cond1#(true(),x,y) -> gr#(x,0())
   cond1#(true(),x,y) -> cond2#(gr(x,0()),x,y)
   cond2#(true(),x,y) -> p#(x)
   cond2#(true(),x,y) -> add#(x,y)
   cond2#(true(),x,y) -> gr#(add(x,y),0())
   cond2#(true(),x,y) -> cond1#(gr(add(x,y),0()),p(x),y)
   cond2#(false(),x,y) -> gr#(y,0())
   cond2#(false(),x,y) -> cond3#(gr(y,0()),x,y)
   cond3#(true(),x,y) -> p#(y)
   cond3#(true(),x,y) -> add#(x,y)
   cond3#(true(),x,y) -> gr#(add(x,y),0())
   cond3#(true(),x,y) -> cond1#(gr(add(x,y),0()),x,p(y))
   cond3#(false(),x,y) -> add#(x,y)
   cond3#(false(),x,y) -> gr#(add(x,y),0())
   cond3#(false(),x,y) -> cond1#(gr(add(x,y),0()),x,y)
   gr#(s(x),s(y)) -> gr#(x,y)
   add#(s(x),y) -> add#(x,y)
  TRS:
   cond1(true(),x,y) -> cond2(gr(x,0()),x,y)
   cond2(true(),x,y) -> cond1(gr(add(x,y),0()),p(x),y)
   cond2(false(),x,y) -> cond3(gr(y,0()),x,y)
   cond3(true(),x,y) -> cond1(gr(add(x,y),0()),x,p(y))
   cond3(false(),x,y) -> cond1(gr(add(x,y),0()),x,y)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y)) -> gr(x,y)
   add(0(),x) -> x
   add(s(x),y) -> s(add(x,y))
   p(0()) -> 0()
   p(s(x)) -> x
  Open