#5217 ⟨a, b | aabbaab=baba⟩

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^-1ab^-1a^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = a, φ(b) = b^-1a^-1

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(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aabbaab=baba reversed:bc/a aab=c morph:3/0
babc=cbcab
bacbc=cbcba
baba=cbc
aab=c
aacbc=caba

1 unique, 1 total

Σ	#	Presentation	Properties
11	5923	⟨a, b \| abbaab=babaa⟩	Can Inf