#4234 ⟨a, b | abaaaabab=ba⟩

Properties

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

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.

# ab:abaaaabab=ba reversed:ac/b ba=c magic:0
acaaacc=ca
acaaacb=c
ba=c
bc=ccaaacb

3 unique, 3 total

Σ	#	Presentation	Properties
9	961	⟨a, b \| aabbbab=ba⟩	Can Inf
10	2327	⟨a, b \| ababaab=bba⟩	Can Inf
10	2752	⟨a, b \| baaba=abbab⟩	Can Inf