MAYBE

Problem:
 nonZero(0()) -> false()
 nonZero(s(x)) -> true()
 p(0()) -> 0()
 p(s(x)) -> x
 id_inc(x) -> x
 id_inc(x) -> s(x)
 random(x) -> rand(x,0())
 rand(x,y) -> if(nonZero(x),x,y)
 if(false(),x,y) -> y
 if(true(),x,y) -> rand(p(x),id_inc(y))

Proof:
 DP Processor:
  DPs:
   random#(x) -> rand#(x,0())
   rand#(x,y) -> nonZero#(x)
   rand#(x,y) -> if#(nonZero(x),x,y)
   if#(true(),x,y) -> id_inc#(y)
   if#(true(),x,y) -> p#(x)
   if#(true(),x,y) -> rand#(p(x),id_inc(y))
  TRS:
   nonZero(0()) -> false()
   nonZero(s(x)) -> true()
   p(0()) -> 0()
   p(s(x)) -> x
   id_inc(x) -> x
   id_inc(x) -> s(x)
   random(x) -> rand(x,0())
   rand(x,y) -> if(nonZero(x),x,y)
   if(false(),x,y) -> y
   if(true(),x,y) -> rand(p(x),id_inc(y))
  Open