#5317 ⟨a, b | abaabab=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^-1a^-1b^-1⟩
- Embedding: φ(a) = ba, φ(b) = a^-1b^-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 = ba
Reduction order:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abaabab=baba reversed:ac/b ba=c morph:2/0
acacc=cca
acacb=cc
ba=c
bcc=ccacb

7 unique, 7 total

Σ	#	Presentation	Properties
7	258	⟨a, b \| aabb=baa⟩	Can Inf
8	525	⟨a, b \| aabab=baa⟩	Can Inf
9	1065	⟨a, b \| aabaab=baa⟩	Can Inf
9	1217	⟨a, b \| aabab=baba⟩	Can Inf
10	2211	⟨a, b \| aabaaab=baa⟩	Can Inf
11	4593	⟨a, b \| aabaaaab=baa⟩	Can Inf
11	5663	⟨a, b \| aabaab=baaba⟩	Can Inf