MAYBE

Problem:
 minus(0(),x) -> 0()
 minus(s(x),0()) -> s(x)
 minus(s(x),s(y)) -> minus(x,y)
 mod(x,0()) -> 0()
 mod(x,s(y)) -> if(lt(x,s(y)),x,s(y))
 if(true(),x,y) -> x
 if(false(),x,y) -> mod(minus(x,y),y)
 gcd(x,0()) -> x
 gcd(0(),s(y)) -> s(y)
 gcd(s(x),s(y)) -> gcd(mod(s(x),s(y)),mod(s(y),s(x)))
 lt(x,0()) -> false()
 lt(0(),s(x)) -> true()
 lt(s(x),s(y)) -> lt(x,y)

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   mod#(x,s(y)) -> lt#(x,s(y))
   mod#(x,s(y)) -> if#(lt(x,s(y)),x,s(y))
   if#(false(),x,y) -> minus#(x,y)
   if#(false(),x,y) -> mod#(minus(x,y),y)
   gcd#(s(x),s(y)) -> mod#(s(y),s(x))
   gcd#(s(x),s(y)) -> mod#(s(x),s(y))
   gcd#(s(x),s(y)) -> gcd#(mod(s(x),s(y)),mod(s(y),s(x)))
   lt#(s(x),s(y)) -> lt#(x,y)
  TRS:
   minus(0(),x) -> 0()
   minus(s(x),0()) -> s(x)
   minus(s(x),s(y)) -> minus(x,y)
   mod(x,0()) -> 0()
   mod(x,s(y)) -> if(lt(x,s(y)),x,s(y))
   if(true(),x,y) -> x
   if(false(),x,y) -> mod(minus(x,y),y)
   gcd(x,0()) -> x
   gcd(0(),s(y)) -> s(y)
   gcd(s(x),s(y)) -> gcd(mod(s(x),s(y)),mod(s(y),s(x)))
   lt(x,0()) -> false()
   lt(0(),s(x)) -> true()
   lt(s(x),s(y)) -> lt(x,y)
  Usable Rule Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    mod#(x,s(y)) -> lt#(x,s(y))
    mod#(x,s(y)) -> if#(lt(x,s(y)),x,s(y))
    if#(false(),x,y) -> minus#(x,y)
    if#(false(),x,y) -> mod#(minus(x,y),y)
    gcd#(s(x),s(y)) -> mod#(s(y),s(x))
    gcd#(s(x),s(y)) -> mod#(s(x),s(y))
    gcd#(s(x),s(y)) -> gcd#(mod(s(x),s(y)),mod(s(y),s(x)))
    lt#(s(x),s(y)) -> lt#(x,y)
   TRS:
    lt(0(),s(x)) -> true()
    lt(s(x),s(y)) -> lt(x,y)
    lt(x,0()) -> false()
    minus(0(),x) -> 0()
    minus(s(x),0()) -> s(x)
    minus(s(x),s(y)) -> minus(x,y)
    mod(x,s(y)) -> if(lt(x,s(y)),x,s(y))
    if(true(),x,y) -> x
    if(false(),x,y) -> mod(minus(x,y),y)
    mod(x,0()) -> 0()
   Open