NO
Rewrite Rules:
   [ le(0,?y) -> true,
     le(s(?x),0) -> false,
     le(s(?x),s(?y)) -> le(?x,?y),
     if(true,?x,?y) -> ?x,
     if(false,?x,?y) -> ?y,
     min(?x,?y) -> if(le(?x,?y),?x,?y),
     le(min(?x,?y),?x) -> true,
     le(min(?x,?y),?y) -> true ]
Apply Direct Methods...
Inner CPs:
   [ le(if(le(?x_5,?y_5),?x_5,?y_5),?x_5) = true,
     le(if(le(?x_5,?y_5),?x_5,?y_5),?y_5) = true ]
Outer CPs:
   [ true = true ]
not Overlay, check Termination...
Terminating, not WCR
Knuth & Bendix
Direct Methods: not CR

Final result: not CR
new/min4.trs: Success(not CR)
(10 msec.)