#5667 ⟨a, b | aabaab=babba⟩

Properties

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

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:aabaab=babba reversed:bc/a aab=c morph:3/0
babbc=ccab
babcc=ccbba
babba=cc
aab=c
aacc=cabba

2 unique, 2 total

Σ	#	Presentation	Properties
11	4145	⟨a, b \| aababbbab=ba⟩	Can Inf
11	4641	⟨a, b \| aababaab=bba⟩	Can Inf