#71 ⟨a, b | ababba=1⟩

Properties

Sum of relation sides is 6
Infinite non-Abelian group
Element a has infinite order
Inverses of generators:
- a^-1 = db
- b^-1 = ad
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aabab^-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(d) = deg(c) = 0, d < c; deg(b) = 1; deg(a) = 2
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:ababba=1 reversed:dc/b/a ba=c,bca=d morph:2/0,3/0
cd=1
dc=1
bd=ccb
bc=ddb
ba=c
ac=dad
add=ca
adb=1

1 unique, 1 total

Σ	#	Presentation	Properties
5	39	⟨a, b \| aaba=b⟩	Can Inf

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

7 total

Σ	#	Presentation	Mapping
6	72	⟨a, b \| abbaab=1⟩	φ(a) = a, φ(b) = dbab
9	660	⟨a, b \| aabaababa=1⟩	φ(a) = a, φ(b) = dbdbab
9	665	⟨a, b \| aababaaab=1⟩	φ(a) = a, φ(b) = dbdbab
9	666	⟨a, b \| aababaaba=1⟩	φ(a) = dbab, φ(b) = addbaa
9	699	⟨a, b \| abaaabaab=1⟩	φ(a) = a, φ(b) = dbdbab
9	700	⟨a, b \| abaaababa=1⟩	φ(a) = dbab, φ(b) = addbaa
9	703	⟨a, b \| abaabaaab=1⟩	φ(a) = dbab, φ(b) = addbaa