⟨a, b | aaaabababba=1⟩

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Monoids with two generators and one relation

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaaaa=c
2. bababb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[13]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[12]
5.	a⁵ ⇒ c	[2]
6.	bcba ⇒ ab²c	[21]
7.	b²a⁴ ⇒ a⁴dbcb	[26]
8.	bab²c ⇒ a³(ab)³	[17]
9.	b(ab)²d ⇒ adbab²	[14]
10.	bab²ac ⇒ a⁴(ba)³	[19]
11.	(ba)³d ⇒ adbab²a	[15]
12.	bab²a²c ⇒ a⁴(ba)³a	[28]
13.	(ba)³ad ⇒ adbab²a²	[27]
14.	bab²a³c ⇒ a³(ab)³a³	[30]
15.	(ba)³a²d ⇒ adbab²a³	[29]
16.	(ba)³a³ ⇒ adb(bc)²	[32]
17.	(ba)²b² ⇒ d	[3]
18.	(b²c)² ⇒ a⁴dba⁴cb(ab)²	[34]
19.	b²cb²ac ⇒ a⁴dba⁴c(ba)³	[35]
20.	b²cb²a²c ⇒ a⁴dba⁴c(ba)³a	[36]
21.	b²cb²a³c ⇒ a⁴dba⁴c(ba)³a²	[37]

# ab:aaaabababba=1 reversed:cda/b aaaaa=c,bababb=d magic:0 dc=1 cd=1 ca=ac da=ad aaaaa=c bcba=abbc bbaaaa=aaaadbcb babbc=aaaababab bababd=adbabb babbac=aaaabababa bababad=adbabba babbaac=aaaabababaa bababaad=adbabbaa babbaaac=aaaabababaaa bababaaad=adbabbaaa bababaaaa=adbbcbc bababb=d bbcbbc=aaaadbaaaacbabab bbcbbac=aaaadbaaaacbababa bbcbbaac=aaaadbaaaacbababaa bbcbbaaac=aaaadbaaaacbababaaa

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

Σ	#	Presentation	Mapping
11	2938	⟨a, b \| aaabababbaa=1⟩	φ(a) = a, φ(b) = b
11	3250	⟨a, b \| ababbaaaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2938

⟨a, b | aaabababbaa=1⟩

φ(a) = a, φ(b) = b

3250

⟨a, b | ababbaaaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2860 ⟨a, b \| aaaabababab=1⟩
Next:	#2862 ⟨a, b \| aaaabababbb=1⟩

#2861 ⟨a, b | aaaabababba=1⟩

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Properties

Rewriting system

Isomorphic instances