⟨a, b | aababababba=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(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
Auxiliary generators:
1. aaa=c
2. babababb=d
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	dc ⇒ 1	[10]
2.	cd ⇒ 1	[8]
3.	ca ⇒ ac	[5]
4.	da ⇒ ad	[9]
5.	a³ ⇒ c	[2]
6.	bcba ⇒ ab²c	[18]
7.	b²a² ⇒ a²dbcb	[23]
8.	(ba)²b²c ⇒ a(ab)⁴	[14]
9.	b(ab)³d ⇒ ad(ba)²b²	[11]
10.	(ba)²b²ac ⇒ a²(ba)⁴	[16]
11.	(ba)⁴d ⇒ ad(ba)²b²a	[12]
12.	(ba)⁴a ⇒ adbab(bc)²	[26]
13.	(ba)³b² ⇒ d	[3]
14.	ba(b²c)² ⇒ a²dba²cb(ab)³	[28]
15.	bab²cb²ac ⇒ a²dba²c(ba)⁴	[30]
16.	(b²c)³ ⇒ a²d(ba²)²cb(ab)³	[32]
17.	b²(cb²)²ac ⇒ a²d(ba²)²c(ba)⁴	[33]

# ab:aababababba=1 reversed:cda/b aaa=c,babababb=d magic:0 dc=1 cd=1 ca=ac da=ad aaa=c bcba=abbc bbaa=aadbcb bababbc=aabababab babababd=adbababb bababbac=aababababa babababad=adbababba babababaa=adbabbcbc babababb=d babbcbbc=aadbaacbababab babbcbbac=aadbaacbabababa bbcbbcbbc=aadbaabaacbababab bbcbbcbbac=aadbaabaacbabababa

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

Σ	#	Presentation	Mapping
11	3245	⟨a, b \| abababbaaab=1⟩	φ(a) = a, φ(b) = b
11	3251	⟨a, b \| ababbaaabab=1⟩	φ(a) = a, φ(b) = b

Presentation

Mapping

3245

⟨a, b | abababbaaab=1⟩

φ(a) = a, φ(b) = b

3251

⟨a, b | ababbaaabab=1⟩

φ(a) = a, φ(b) = b

Up:	Monoids with two generators and one relation
Prev:	#3067 ⟨a, b \| aababababab=1⟩
Next:	#3069 ⟨a, b \| aabababbaab=1⟩

#3068 ⟨a, b | aababababba=1⟩

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Properties

Rewriting system

Isomorphic instances