#3802 ⟨a, b | abbaaabaab=b⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

Rewriting system

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(b) = 0, c < b; deg(a) = 1
Auxiliary generators:
1. aaab=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	cb² ⇒ bcb	[10]
2.	(cb)² ⇒ b	[7]
3.	cbab ⇒ bcab	[9]
4.	cbcab ⇒ ab	[6]
5.	ab³ ⇒ b²cabcb	[14]
6.	ab²cb ⇒ b²cab	[11]
7.	cba²b ⇒ bca²b	[8]
8.	cbca²b ⇒ a²b	[4]
9.	ab²ab ⇒ b²(cab)²	[13]
10.	ab²cab ⇒ b²ca²b	[5]
11.	a³b ⇒ c	[2]
12.	ab²a²b ⇒ b(bca)²ab	[12]
13.	ab²ca²b ⇒ b	[3]

# ab:abbaaabaab=b reversed:cb/a aaab=c morph:4/0
cbb=bcb
cbcb=b
cbab=bcab
cbcab=ab
abbb=bbcabcb
abbcb=bbcab
cbaab=bcaab
cbcaab=aab
abbab=bbcabcab
abbcab=bbcaab
aaab=c
abbaab=bbcabcaab
abbcaab=b