#4487 ⟨a, b | aaabaaab=baa⟩

Properties

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

# ab:aaabaaab=baa reversed:ac/b baa=c magic:0
aaacac=caa
aaacab=c
bc=cacab
baa=c
bac=caacab

5 unique, 5 total

Σ	#	Presentation	Properties
8	511	⟨a, b \| aaabb=baa⟩	Can Inf
8	582	⟨a, b \| baaa=aabb⟩	Can Inf
9	1045	⟨a, b \| aaabab=baa⟩	Can Inf
10	2163	⟨a, b \| aaabaab=baa⟩	Can Inf
11	5875	⟨a, b \| ababab=babaa⟩	Can Inf

4 unique, 4 total

Σ	#	Presentation	Properties
9	1215	⟨a, b \| aabab=baaa⟩	Can Inf
10	2487	⟨a, b \| aabaab=baaa⟩	Can Inf
11	5125	⟨a, b \| aabaaab=baaa⟩	Can Inf
11	5185	⟨a, b \| aababab=baba⟩	Can Inf