#4773 ⟨a, b | abaaabab=bba⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabab^-1ab^-1a^-1bb⟩
- Anti-isomorphic embedding: φ(a) = a, φ(b) = ba^-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 ⇒ aca²cb	[4]

# ab:abaaabab=bba reversed:ac/b ba=c morph:2/0
ba=c
bc=acaacb

1 unique, 1 total

Σ	#	Presentation	Properties
11	4118	⟨a, b \| aababaabb=ba⟩	Can Inf

1 unique, 1 total

Σ	#	Presentation	Properties
11	4802	⟨a, b \| abaabbab=baa⟩	Can Inf