⟨a, b | abbaaaabaab=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(a) = deg(d) = 0, a < d; deg(c) = deg(b) = 1, c < b
Auxiliary generators:
1. ababb=c
2. abac=d
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ad ⇒ da	[20]
2.	da³ ⇒ 1	[12]
3.	bac ⇒ d²a²	[21]
4.	ca⁴b ⇒ da²	[17]
5.	b² ⇒ ca³c	[9]
6.	bab ⇒ da(ac)²a⁴	[26]
7.	ba²b ⇒ dca⁵ca³	[35]
8.	ba⁴b ⇒ aca⁴ca²	[39]
9.	ca³cac ⇒ bd²a²	[22]
10.	ca(a³c)² ⇒ da²b	[23]
11.	ca(a⁴c)² ⇒ a³bda	[49]
12.	caca⁵c ⇒ abd	[31]
13.	ca³cb ⇒ bca³c	[10]
14.	ca³cab ⇒ bda(ac)²a⁴	[27]
15.	ca³ca²b ⇒ bdca⁵ca³	[36]
16.	ca⁴ca²b ⇒ da²ba(a³c)²	[30]
17.	ca⁴ca³b ⇒ da²ba³caca⁴	[40]
18.	ca⁵ca³b ⇒ a³ba²ca³c	[45]
19.	caca⁵b ⇒ abcaca⁴	[48]
20.	(ca⁵)²b ⇒ a³bd(a²ca³)²	[52]
21.	caca⁶b ⇒ abdaca⁵ca³	[51]
22.	ca⁴ca⁶b ⇒ da²ba(a⁴c)²a²	[43]
23.	ca⁵ca⁷b ⇒ a³b(a³ca)²a	[46]
24.	caca⁸b ⇒ ab(a²ca²)²	[44]

# ab:abbaaaabaab=1 reversed:ad/cb ababb=c,abac=d morph:5/1,4/0 ad=da daaa=1 bac=ddaa caaaab=daa bb=caaac bab=daacacaaaa baab=dcaaaaacaaa baaaab=acaaaacaa caaacac=bddaa caaaacaaac=daab caaaaacaaaac=aaabda cacaaaaac=abd caaacb=bcaaac caaacab=bdaacacaaaa caaacaab=bdcaaaaacaaa caaaacaab=daabaaaacaaac caaaacaaab=daabaaacacaaaa caaaaacaaab=aaabaacaaac cacaaaaab=abcacaaaa caaaaacaaaaab=aaabdaacaaaaacaaa cacaaaaaab=abdacaaaaacaaa caaaacaaaaaab=daabaaaaacaaaacaa caaaaacaaaaaaab=aaabaaacaaaacaa cacaaaaaaaab=abaacaaaacaa

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#3271 ⟨a, b | abbaaaabaab=1⟩

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