#4719 ⟨a, b | aabbbaab=baa⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element ba has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbab^-1b^-1a^-1bb⟩
- Embedding: φ(a) = b, φ(b) = a

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 = bbbc
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:aabbbaab=baa b/d/c/a aa=c,bbbc=d morph:2/1,4/0
ddb=bd
cdbdbdb=d
bc=cdb
dc=cdddddddd
da=bbbac
ca=ac
cdba=bac
cdbdba=bbac
aa=c