#2487 ⟨a, b | aabaab=baaa⟩

Properties

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

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 = aab
Reduction order:
- Left-to-right 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.

# ab:aabaab=baaa ac/b aab=c morph:3/0
caaa=aacc
baaa=cc
aab=c
ccb=bac
ccab=baac

6 unique, 6 total

Σ	#	Presentation	Properties
8	511	⟨a, b \| aaabb=baa⟩	Can Inf
8	582	⟨a, b \| baaa=aabb⟩	Can Inf
9	1045	⟨a, b \| aaabab=baa⟩	Can Inf
10	2163	⟨a, b \| aaabaab=baa⟩	Can Inf
11	4487	⟨a, b \| aaabaaab=baa⟩	Can Inf
11	5875	⟨a, b \| ababab=babaa⟩	Can Inf

3 unique, 3 total

Σ	#	Presentation	Properties
9	1215	⟨a, b \| aabab=baaa⟩	Can Inf
11	5125	⟨a, b \| aabaaab=baaa⟩	Can Inf
11	5185	⟨a, b \| aababab=baba⟩	Can Inf