#4789 ⟨a, b | abaabaab=bba⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbaba^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = ba, φ(b) = b^-1a^-1b^-1

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 = ba
Reduction order:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	ba ⇒ c	[2]
2.	bc ⇒ a(ca)²b	[4]

# ab:abaabaab=bba reversed:ac/b ba=c morph:2/0
ba=c
bc=acacab

3 unique, 3 total

Σ	#	Presentation	Properties
9	919	⟨a, b \| aaabbab=ba⟩	Can Inf
9	1253	⟨a, b \| abaab=bbba⟩	Can Inf
11	3988	⟨a, b \| aaababaab=ba⟩	Can Inf

2 unique, 2 total

Σ	#	Presentation	Properties
11	4184	⟨a, b \| aabbabbab=ba⟩	Can Inf
11	5347	⟨a, b \| ababaab=baaa⟩	Can Inf