#2257 ⟨a, b | aabbaab=baa⟩

Properties

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

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 = aa
2. d = bbc
Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(d) = 1; deg(c) = 2; deg(a) = 3
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aabbaab=baa b/d/c/a aa=c,bbc=d morph:2/0,3/0
ddb=bd
cdbdb=d
bc=cdb
dc=cdddd
da=bbac
ca=ac
cdba=bac
aa=c