NO
Rewrite Rules:
   [ min(0,?y) -> 0,
     min(?x,0) -> 0,
     min(s(?x),s(?y)) -> s(min(?x,?y)),
     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(0,0) = true,
     le(0,?x_1) = true,
     le(s(min(?x_2,?y_2)),s(?x_2)) = true,
     le(if(le(?x_8,?y_8),?x_8,?y_8),?x_8) = true,
     le(0,?y) = true,
     le(0,0) = true,
     le(s(min(?x_2,?y_2)),s(?y_2)) = true,
     le(if(le(?x_8,?y_8),?x_8,?y_8),?y_8) = true ]
Outer CPs:
   [ 0 = 0,
     0 = if(le(0,?y),0,?y),
     0 = if(le(?x_1,0),?x_1,0),
     s(min(?x_2,?y_2)) = if(le(s(?x_2),s(?y_2)),s(?x_2),s(?y_2)),
     true = true ]
not Overlay, check Termination...
Terminating, not WCR
Knuth & Bendix
Direct Methods: not CR

Final result: not CR
new/min2.trs: Success(not CR)
(19 msec.)