#4476 ⟨a, b, c | aba=1, cbcc=b⟩

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element a has infinite order
Inverses of generators:
- a^-1 = da³
- b^-1 = a²
- c^-1 = da²c²a²
- d^-1 = a⁴
Reduced group presentation: ⟨a, b | aabbab^-1b^-1⟩
- Isomorphism: φ(a) = b, φ(b) = b^-1b^-1, φ(c) = a

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

# abc:aba=1,cbcc=b ac/db bb=d morph:2/6
ccaac=aa
ccaaaa=aacaac
daaaa=1
ad=da
cd=dcccc
b=daa

1 unique, 1 total

Σ	#	Presentation	Properties
8	5269	⟨a, b, c \| aa=b, cbcc=b⟩	Can Inf