#1513 ⟨a, b | ababababba=1⟩

Properties

Sum of relation sides is 10
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 | aaaabab^-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 = acccb
Reduction order:
- Left-to-right 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:ababababba=1 cd/ab ba=c,acccb=d morph:2/0,5/0
cd=1
dc=1
ca=adddd
da=acccc
ddb=ccbc
cccb=dbd
adb=1
ba=c

1 unique, 1 total

Σ	#	Presentation	Properties
7	166	⟨a, b \| aaaaba=b⟩	Can Inf

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

2 total

Σ	#	Presentation	Mapping
10	1514	⟨a, b \| abababbaab=1⟩	φ(a) = a, φ(b) = dbab
10	1518	⟨a, b \| ababbaabab=1⟩	φ(a) = a, φ(b) = dbab