MAYBE

Problem:
 minus(x,y) -> cond(gt(x,y),x,y)
 cond(false(),x,y) -> 0()
 cond(true(),x,y) -> s(minus(x,s(y)))
 gt(0(),v) -> false()
 gt(s(u),0()) -> true()
 gt(s(u),s(v)) -> gt(u,v)

Proof:
 DP Processor:
  DPs:
   minus#(x,y) -> gt#(x,y)
   minus#(x,y) -> cond#(gt(x,y),x,y)
   cond#(true(),x,y) -> minus#(x,s(y))
   gt#(s(u),s(v)) -> gt#(u,v)
  TRS:
   minus(x,y) -> cond(gt(x,y),x,y)
   cond(false(),x,y) -> 0()
   cond(true(),x,y) -> s(minus(x,s(y)))
   gt(0(),v) -> false()
   gt(s(u),0()) -> true()
   gt(s(u),s(v)) -> gt(u,v)
  Open