#5127 ⟨a, b | aabaaab=baba⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabaaba^-1b^-1b^-1⟩
- Embedding: φ(a) = a, φ(b) = a^-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 = aabaaa
Reduction order:
- Right-to-left recursive path with deg(a) = 0; deg(c) = deg(b) = 1, c < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aabaaab=baba reversed:a/cb aabaaa=c morph:6/0
aabaaa=c
cbaaa=aabac
cabaaa=aabaac
baba=cb
babca=caabac
ccbaa=babc
cbba=bacb
cbbca=bacaabac

2 unique, 2 total

Σ	#	Presentation	Properties
9	1067	⟨a, b \| aabaab=bba⟩	Can Inf
10	1975	⟨a, b \| aababbab=ba⟩	Can Inf