#1983 ⟨a, b | aabbaaab=ba⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbaab^-1a^-1b⟩
- Anti-isomorphic embedding: φ(a) = a, φ(b) = b

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

# ab:aabbaaab=ba reversed:cd/ab ba=c,ab=d morph:2/2,2/1
ac=da
adcc=ccad
bc=cdcad
bd=cb
adcad=c
ba=c
ab=d

1 unique, 1 total

Σ	#	Presentation	Properties
10	2347	⟨a, b \| abbaaab=baa⟩	Can Inf