#3495 ⟨a, b, c | bb=aa, cac=b⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbabb⟩
- Embedding: φ(a) = b^-1b^-1a^-1, φ(b) = a, φ(c) = ab

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

Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:bb=aa,cac=b ac/b - -
cacaa=aacac
caccac=aa
caccaaa=aaaccac
b=cac

2 unique, 9 total

Σ	#	Presentation	Properties	φ
8	2183	⟨a, b, c \| aabb=1, bcac=1⟩	Grp Inf	7
8	3599	⟨a, b, c \| bb=aa, cc=ab⟩	Can Inf