I was going through [this][1] paper by Tanaka but I am stuck at the Proposition 4.1 given below [![enter image description here][2]][2]. I just cannot make sense of the first two lines of the proof What does it mean when he says S-reducible and reducible? I tried searching online also but could not find anything, nor does the author refer to anything.

Can someone help me with this?

Thanks and regards in advance.

  [1]: https://jkms.kms.or.kr/journal/view.html?doi=10.4134/JKMS.2012.49.2.251
  [2]: https://i.sstatic.net/cxzib.png