⟨a, b | aababbaabba=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(b) = 0, c < d < b; deg(a) = 1
Auxiliary generators:
1. bb=c
2. aabbaaaba=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[41]
2.	cd ⇒ 1	[35]
3.	cb ⇒ bc	[5]
4.	db ⇒ bd	[40]
5.	b² ⇒ c	[2]
6.	a³b ⇒ dabaca	[54]
7.	abacab ⇒ ca³c	[56]
8.	abaca²c ⇒ b(aca)²	[53]
9.	(aca)²d ⇒ bdabaca²	[63]
10.	abaca²bc ⇒ b(aca)²b	[58]
11.	(aca)²bd ⇒ bdabaca²b	[62]
12.	a(ca²)²d ⇒ bda²baca²	[68]
13.	a(ca²)²b ⇒ ba²ca³c	[66]
14.	a²baca²b ⇒ ca²ca³	[61]
15.	a³(ca)²b ⇒ dabac²a³c	[57]
16.	aca²ca³ ⇒ bd	[46]
17.	a³caca²c ⇒ d(ab)²c(aca)²	[59]
18.	a³caca²bc ⇒ d(ab)²c(aca)²b	[70]
19.	a²ca⁴cab ⇒ da²b(ac)²a³c	[71]
20.	(a²ca²)²c ⇒ da(ab)²ca(ca²)²	[74]
21.	(a²ca²)²b ⇒ da²bac²a²ca³	[73]
22.	(a²ca)²ca²b ⇒ bda(ca²c)²a³	[76]

# ab:aababbaabba=1 reversed:cdb/a bb=c,aabbaaaba=d magic:1 dc=1 cd=1 cb=bc db=bd bb=c aaab=dabaca abacab=caaac abacaac=bacaaca acaacad=bdabacaa abacaabc=bacaacab acaacabd=bdabacaab acaacaad=bdaabacaa acaacaab=baacaaac aabacaab=caacaaa aaacacab=dabaccaaac acaacaaa=bd aaacacaac=dababcacaaca aaacacaabc=dababcacaacab aacaaaacab=daabacacaaac aacaaaacaac=daababcacaacaa aacaaaacaab=daabaccaacaaa aacaaacacaab=bdacaaccaacaaa

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

Σ	#	Presentation	Mapping
11	3274	⟨a, b \| abbaaababba=1⟩	φ(a) = a, φ(b) = b
11	3281	⟨a, b \| abbaabbaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3274

⟨a, b | abbaaababba=1⟩

φ(a) = a, φ(b) = b

3281

⟨a, b | abbaabbaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3077 ⟨a, b \| aababbaabab=1⟩
Next:	#3079 ⟨a, b \| aababbabaab=1⟩

#3078 ⟨a, b | aababbaabba=1⟩

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Properties

Rewriting system

Isomorphic instances