#3744 ⟨a, b | abaabbaaba=b⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabbaab^-1a^-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 = abbaaba
Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(a) = 1; deg(b) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abaabbaaba=b c/a/b abbaaba=c morph:7/0
abac=b
abbc=ccbaaba
abbac=cbacaaba
abbb=ccac
abbab=cc
abbaabc=cbbaaba
abbaaba=c
abbaabb=cbac

2 unique, 2 total

Σ	#	Presentation	Properties
9	1085	⟨a, b \| aabbaa=bab⟩	Can Inf
11	5172	⟨a, b \| aababaa=baab⟩	Can Inf