ö-insertion:

z – devoicing:

dagz à dagz

	ö-ins	z-dev	lex	surf
1	0	0	d	d
2	0	0	a	a
3	0	0	g	g
4	0	0	z	z
5	1	0	#	#
6	0	0

At step 4, we can’t do a z:s because we’re at state 0 in z-devoicing.

At step 4, we can’t do an ö-insertion because we’re at state 0 in ö-insertion.

cQtz à cQts

	ö-ins	z-dev	lex	surf
1	0	0	c	c
2	0	1	Q	Q
3	0	0	t	t
4	0	1	z	s
5	1	2	#	#
6	0	0

At step 4, we do a z:s. This is allowed at state 0 of ö-insertion because we’re only interested in making sure that there’s a sibilant at surface structure; we let other rules change it if they need to.

At step 4, we can’t do a z:z because we’re at state 1 in z-devoicing. We can’t do ö-insertion because we’re at state 0 there.

faksz à faksöz

	ö-ins	z-dev	lex	surf
1	0	0	f	f
2	0	1	a	a
3	0	0	k	k
4	0	1	s	s
5	1	1	E	ö
6	2	0	z	z
7	3	0	#	#
8	0	0

In step 5 we can take an E:ö arc in z-devoicing – it is the “other” arc. We can’t take z:z because we’re in state 1 in z-devoicing. We can’t take z:s because we’re in state 1 of ö-insertion, which should prevent two sibilants at the end of the word.

In step 6, we can’t take z:s because we’re in state 0 in z-devoicing.

flapping:

Canadian raising:

raid¨` à raiR¨`

	flap	rais	lex	surf
1	0	0	r	r
2	0	0	ai	ai
3	1	2	d	R
4	2	0	¨	¨
5	0	0

At step 2, we can’t take an aI:ÃI arc, because that would leave us at state 1 in raising. There’s no way out of there with an input d.

At step 3, we couldn’t take the d:d arc, because that would leave us at state 3 in flapping. There’s no way out of there with an unstressed vowel.

rait¨` à rÃiR¨`

	flap	rais	lex	surf
1	0	0	r	r
2	0	0	ai	Ãi
3	1	1	t	R
4	2	0	¨	¨
5	0	0

At step 2 we can take the aI:ÃI arc in flapping because it’s an other. We can’t just take the ai:ai arc, because that would leave us in state 2 in Canadian raising. There’s no way out of there with a surface voiceless sound.