⟨a, b | aaabbababba=1⟩

Up:

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Auxiliary generators:
1. c = aaaa
2. d = bbababb
Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cd ⇒ 1	[16]
2.	dc ⇒ 1	[19]
3.	ac ⇒ ca	[5]
4.	ad ⇒ da	[20]
5.	a⁴ ⇒ c	[2]
6.	ab²cb ⇒ bcb²a	[42]
7.	abab² ⇒ cb²abda	[23]
8.	a³b²ab ⇒ bab²a³	[29]
9.	a³bcb² ⇒ cb²cbda³	[41]
10.	cb²(ab)² ⇒ bcb(ba)²	[39]
11.	dbcb²ab ⇒ b²(ab)²da³	[27]
12.	cab²(ab)² ⇒ abcb(ba)²	[43]
13.	dabcb²ab ⇒ ab²(ab)²da³	[46]
14.	ca²b²(ab)² ⇒ a²bcb(ba)²	[45]
15.	da²bcb²ab ⇒ a²b²(ab)²da³	[48]
16.	b²cb²ab ⇒ da³	[32]
17.	a³b³cb² ⇒ bab²a³bcbda³	[36]
18.	(cb²ab)² ⇒ bcb²aba²b²a³	[49]
19.	d(bcb²)² ⇒ b²(ab)²da³bcbda³	[53]
20.	cab²abcb²ab ⇒ abcb²aba²b²a³	[50]
21.	da(bcb²)² ⇒ ab²(ab)²da³bcbda³	[55]
22.	ca²b²abcb²ab ⇒ a²bcb²aba²b²a³	[54]
23.	da²(bcb²)² ⇒ a²b²(ab)²da³bcbda³	[56]
24.	b(bcb²)² ⇒ da³bcbda³	[37]
25.	cb²a(bcb²)² ⇒ bcb²aba²b²a³bcbda³	[58]
26.	cab²a(bcb²)² ⇒ abcb²aba²b²a³bcbda³	[59]
27.	ca²b²a(bcb²)² ⇒ a²bcb²aba²b²a³bcbda³	[60]

# ab:aaabbababba=1 cda/b aaaa=c,bbababb=d magic:0 cd=1 dc=1 ac=ca ad=da aaaa=c abbcb=bcbba ababb=cbbabda aaabbab=babbaaa aaabcbb=cbbcbdaaa cbbabab=bcbbaba dbcbbab=bbababdaaa cabbabab=abcbbaba dabcbbab=abbababdaaa caabbabab=aabcbbaba daabcbbab=aabbababdaaa bbcbbab=daaa aaabbbcbb=babbaaabcbdaaa cbbabcbbab=bcbbabaabbaaa dbcbbbcbb=bbababdaaabcbdaaa cabbabcbbab=abcbbabaabbaaa dabcbbbcbb=abbababdaaabcbdaaa caabbabcbbab=aabcbbabaabbaaa daabcbbbcbb=aabbababdaaabcbdaaa bbcbbbcbb=daaabcbdaaa cbbabcbbbcbb=bcbbabaabbaaabcbdaaa cabbabcbbbcbb=abcbbabaabbaaabcbdaaa caabbabcbbbcbb=aabcbbabaabbaaabcbdaaa

Σ	#	Presentation	Properties
10	2304	⟨a, b \| abaaaba=bbb⟩	Can Inf

Presentation

Properties

2304

⟨a, b | abaaaba=bbb⟩

Can Inf

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

Σ	#	Presentation	Mapping
11	3122	⟨a, b \| aabbababbaa=1⟩	φ(a) = a, φ(b) = daaaab
11	3224	⟨a, b \| abaabbbbaab=1⟩	φ(a) = daaaab, φ(b) = a
11	3238	⟨a, b \| ababaabbbba=1⟩	φ(a) = daaaab, φ(b) = a

Presentation

Mapping

3122

⟨a, b | aabbababbaa=1⟩

φ(a) = a, φ(b) = daaaab

3224

⟨a, b | abaabbbbaab=1⟩

φ(a) = daaaab, φ(b) = a

3238

⟨a, b | ababaabbbba=1⟩

φ(a) = daaaab, φ(b) = a

Up:	Monoid enumeration
Prev:	#2971 ⟨a, b \| aaabbababab=1⟩
Next:	#2974 ⟨a, b \| aaabbabbaab=1⟩

#2972 ⟨a, b | aaabbababba=1⟩

Contents

Properties

Rewriting system

Other submonoids of same group

Isomorphic instances