#4110 ⟨a, b | aababaaab=ba⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabbaaba^-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 = aabab
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:aababaaab=ba reversed:ac/b aabab=c morph:5/0
aacaaacacacaaacac=ca
ba=caaab
bc=cacab
aacaaabb=c

2 unique, 2 total

Σ	#	Presentation	Properties
9	950	⟨a, b \| aabbaab=ba⟩	Can Inf
11	4273	⟨a, b \| abaabbaab=ba⟩	Can Inf

3 unique, 3 total

Σ	#	Presentation	Properties
9	1132	⟨a, b \| abbaab=baa⟩	Can Inf
11	4815	⟨a, b \| ababaaab=baa⟩	Can Inf
11	5922	⟨a, b \| abbaab=baaba⟩	Can Inf