#331 ⟨a, b | abababba=1⟩

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element a has infinite order
Inverses of generators:
- a^-1 = dcb
- b^-1 = cac²
- c^-1 = dc
- d^-1 = c²
Reduced group presentation: ⟨a, b | aaabab^-1⟩
- Isomorphism: φ(a) = b^-1, φ(b) = ba

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

# ab:abababba=1 reversed:cd/ab ba=c,bca=d morph:2/0,3/0
cd=dc
dcc=1
ad=cac
accc=dca
bc=ddcb
bd=ccccccb
ba=c
accb=dc

1 unique, 1 total

Σ	#	Presentation	Properties
6	79	⟨a, b \| aaaba=b⟩	Can Inf

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ	#	Presentation	Mapping
8	332	⟨a, b \| ababbaab=1⟩	φ(a) = a, φ(b) = dcbab