⟨a, b | aaaabaaabba=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. aaaaa=c
2. baaabb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[12]
2.	dc ⇒ 1	[19]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[18]
5.	a⁵ ⇒ c	[2]
6.	cba³b ⇒ bcba³	[25]
7.	dbcb ⇒ ba³bda²	[40]
8.	caba³b ⇒ abcba³	[29]
9.	dabcb ⇒ aba³bda²	[41]
10.	a²bcb ⇒ cb²a²	[39]
11.	a²ba³b ⇒ b²c	[22]
12.	a³b² ⇒ bcbda³	[37]
13.	b²cb ⇒ da²	[35]
14.	cbab² ⇒ (bc)²abd	[28]
15.	cbcab² ⇒ (bc)²a³bda³	[45]
16.	cabab² ⇒ a(bc)²abd	[42]
17.	(cab)²b ⇒ a(bc)²a³bda³	[46]
18.	a²bab² ⇒ b²ca³bd	[36]
19.	a²bcab² ⇒ b²c²bda³	[44]

# ab:aaaabaaabba=1 cda/b aaaaa=c,baaabb=d magic:0 cd=1 dc=1 ac=ca ad=da aaaaa=c cbaaab=bcbaaa dbcb=baaabdaa cabaaab=abcbaaa dabcb=abaaabdaa aabcb=cbbaa aabaaab=bbc aaabb=bcbdaaa bbcb=daa cbabb=bcbcabd cbcabb=bcbcaaabdaaa cababb=abcbcabd cabcabb=abcbcaaabdaaa aababb=bbcaaabd aabcabb=bbccbdaaa

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

Σ	#	Presentation	Mapping
11	2910	⟨a, b \| aaabaaabbaa=1⟩	φ(a) = a, φ(b) = b
11	2954	⟨a, b \| aaabbaaaaab=1⟩	φ(a) = a, φ(b) = b
11	3096	⟨a, b \| aabbaaaaaba=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

2910

⟨a, b | aaabaaabbaa=1⟩

φ(a) = a, φ(b) = b

2954

⟨a, b | aaabbaaaaab=1⟩

φ(a) = a, φ(b) = b

3096

⟨a, b | aabbaaaaaba=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#2844 ⟨a, b \| aaaabaaabab=1⟩
Next:	#2846 ⟨a, b \| aaaabaaabbb=1⟩

#2845 ⟨a, b | aaaabaaabba=1⟩

Quick links

Properties

Rewriting system

Isomorphic instances