MAYBE

Problem:
 cond1(true(),x,y) -> cond2(gr(x,y),x,y)
 cond2(true(),x,y) -> cond1(gr0(x),y,y)
 cond2(false(),x,y) -> cond1(gr0(x),p(x),y)
 gr(0(),x) -> false()
 gr(s(x),0()) -> true()
 gr(s(x),s(y)) -> gr(x,y)
 gr0(0()) -> false()
 gr0(s(x)) -> true()
 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) -> gr0#(x)
   cond2#(true(),x,y) -> cond1#(gr0(x),y,y)
   cond2#(false(),x,y) -> p#(x)
   cond2#(false(),x,y) -> gr0#(x)
   cond2#(false(),x,y) -> cond1#(gr0(x),p(x),y)
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond1(true(),x,y) -> cond2(gr(x,y),x,y)
   cond2(true(),x,y) -> cond1(gr0(x),y,y)
   cond2(false(),x,y) -> cond1(gr0(x),p(x),y)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y)) -> gr(x,y)
   gr0(0()) -> false()
   gr0(s(x)) -> true()
   p(0()) -> 0()
   p(s(x)) -> x
  Open