#2036 ⟨a, b | abaabaab=ba⟩

Properties

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

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:
- 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:abaabaab=ba reversed:ac/b aab=c morph:3/0
accc=ca
aab=c
ba=ccccccab
bc=cccccccccb

2 unique, 2 total

Σ	#	Presentation	Properties
6	99	⟨a, b \| aaab=ba⟩	Can Inf
8	474	⟨a, b \| ababab=ba⟩	Can Inf