#5319 ⟨a, b | abaabab=bbaa⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aababa^-1ba^-1b^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = b, φ(b) = ab^-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 = ab
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=bbaa reversed:ac/b ab=c morph:2/0
ab=c
cbaa=acacc
cbac=acaccb
bbaa=cacc
bbac=caccb

3 unique, 3 total

Σ	#	Presentation	Properties
11	5159	⟨a, b \| aabaabb=baba⟩	Can Inf
11	5722	⟨a, b \| aababb=baaba⟩	Can Inf
11	5771	⟨a, b \| aabbab=bbaba⟩	Can Inf