#4063 ⟨a, b | aabaaaaab=ba⟩

Properties

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

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 = baaaaa
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.

# ab:aabaaaaab=ba reversed:ac/b baaaaa=c morph:6/0
aacc=ca
aacaacaacaacaacb=c
ba=aacb
bc=caccacccaacaacaacb

17 unique, 17 total

Σ	#	Presentation	Properties
6	107	⟨a, b \| aabb=ba⟩	Can Inf
6	121	⟨a, b \| baa=abb⟩	Can Inf
7	217	⟨a, b \| aabab=ba⟩	Can Inf
7	262	⟨a, b \| abab=baa⟩	Can Inf
8	445	⟨a, b \| aabaab=ba⟩	Can Inf
8	541	⟨a, b \| abaab=baa⟩	Can Inf
9	927	⟨a, b \| aabaaab=ba⟩	Can Inf
9	976	⟨a, b \| abaabab=ba⟩	Can Inf
9	1107	⟨a, b \| abaaab=baa⟩	Can Inf
9	1249	⟨a, b \| abaab=baba⟩	Can Inf
10	1937	⟨a, b \| aabaaaab=ba⟩	Can Inf
10	2295	⟨a, b \| abaaaab=baa⟩	Can Inf
11	4242	⟨a, b \| abaaabaab=ba⟩	Can Inf
11	4289	⟨a, b \| ababaabab=ba⟩	Can Inf
11	4757	⟨a, b \| abaaaaab=baa⟩	Can Inf
11	5349	⟨a, b \| ababaab=baba⟩	Can Inf
11	5827	⟨a, b \| abaaab=baaba⟩	Can Inf