YES
Input TRS:
    1: le(x,0()) -> false()
    2: le(0(),s(y)) -> true()
    3: le(s(x),s(y)) -> le(x,y)
    4: min(cons(x,nil())) -> x
    5: min(cons(x,xs)) -> x | min(xs) --> y | le(x,y) --> true()
    6: min(cons(x,xs)) -> y | min(xs) --> y | le(x,y) --> false()
Infeasibility test:
    min(nil()) --> x1
    le(x2,x1) --> true()
Co-Order(NegReal,≥,Sum) ... succeeded.
    le(x1,x2)	weight: (- (/ 37175 2)) + x2
     s(x1)	weight: 0
 false()	weight: (- (/ 37175 2))
  true()	weight: (- (/ 37175 2))
     0()	weight: 0
   nil()	weight: (- (/ 44229 2))
    #(x1,x2)	weight: x2 + x1
   min(x1)	weight: x1
  cons(x1,x2)	weight: 0