Related papers: Termination of log flips in dimension 4

This paper has been withdrawn by author due to an error in the proof.

this paper has been withdrawn by the author due to crucial type errors

This paper has been withdrawn by the author, due to obsolete reference [4], insufficient discussion in sec. 4, and major conceptual error in sec. 5.

This paper has been withdrawn by the author(s), due to a crucial error in eq. 6.

This paper has been withdrawn by the author because eq.(4) and those subsequent are incorrect.

This paper has been withdrawn by the author because there are some typos in proofs.

This paper has been withdrawn by the author due to a crucial problem in Lemma 3. This equation must be changed.

This paper has been withdrawn by the authors due to a gap in the proof of the main result (in 5.3).

This paper has been withdrawn by the author, due a crucial error in the optimization. For the last one month I have been trying to remove the error, but it seems to take a lot of time so I decided to withdraw this paper for the moment.

This paper has been withdrawn by the author due to serious error found in main argument.

Major mistake. The paper has been withdrawn.

This paper has been withdrawn by the author, due to an error in Proposition 2.2.

This paper has been withdrawn by the author due to a crucial error.

The paper is withdrawn.

The paper has been withdrawn.

This paper has been withdrawn by the author, due to an important sign error in Eqn. 2.

This paper has been withdrawn by the author due to an error

This paper was withdrawn by the authors. Lemma 5.1 is wrong.

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

This paper has been withdrawn due to an error, and no further revisions will be made.