⟨a, b | aaababbaaab=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:
- Left-to-right recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaa=c
2. babbaaab=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[4]
2.	dc ⇒ 1	[22]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[24]
5.	a³ ⇒ c	[2]
6.	ab² ⇒ cbabd	[11]
7.	a(ab)² ⇒ b²c	[25]
8.	(cb)²ab ⇒ b(cb)²a	[27]
9.	db(cb)² ⇒ bcbabda²	[31]
10.	cabcbab ⇒ ab(cb)²a	[28]
11.	dab(cb)² ⇒ abcbabda²	[32]
12.	a²b(cb)² ⇒ cb²cba²	[18]
13.	a²bcbab ⇒ b(bc)²	[26]
14.	b²(cb)² ⇒ da²	[17]

# ab:aaababbaaab=1 cda/b aaa=c,babbaaab=d magic:0 cd=1 dc=1 ac=ca ad=da aaa=c abb=cbabd aabab=bbc cbcbab=bcbcba dbcbcb=bcbabdaa cabcbab=abcbcba dabcbcb=abcbabdaa aabcbcb=cbbcbaa aabcbab=bbcbc bbcbcb=daa

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

Σ	#	Presentation	Mapping
11	3022	⟨a, b \| aabaaababba=1⟩	φ(a) = a, φ(b) = b
11	3075	⟨a, b \| aababbaaaba=1⟩	φ(a) = a, φ(b) = b
11	3273	⟨a, b \| abbaaabaaab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3022

⟨a, b | aabaaababba=1⟩

φ(a) = a, φ(b) = b

3075

⟨a, b | aababbaaaba=1⟩

φ(a) = a, φ(b) = b

3273

⟨a, b | abbaaabaaab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2940 ⟨a, b \| aaabababbba=1⟩
Next:	#2942 ⟨a, b \| aaababbaaba=1⟩

#2941 ⟨a, b | aaababbaaab=1⟩

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Properties

Rewriting system

Isomorphic instances