#4593 ⟨a, b | aabaaaab=baa⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabba^-1a^-1b^-1⟩
- Embedding: φ(a) = a, φ(b) = a^-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 = baaaa
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:aabaaaab=baa reversed:ac/b baaaa=c morph:5/1
aacc=caa
aacaacb=c
bc=ccccb
baa=aacb
bac=cacccb

7 unique, 7 total

Σ	#	Presentation	Properties
7	258	⟨a, b \| aabb=baa⟩	Can Inf
8	525	⟨a, b \| aabab=baa⟩	Can Inf
9	1065	⟨a, b \| aabaab=baa⟩	Can Inf
9	1217	⟨a, b \| aabab=baba⟩	Can Inf
10	2211	⟨a, b \| aabaaab=baa⟩	Can Inf
11	5317	⟨a, b \| abaabab=baba⟩	Can Inf
11	5663	⟨a, b \| aabaab=baaba⟩	Can Inf