#1519 ⟨a, b | ababbaabba=1⟩

Properties

Sum of relation sides is 10
Infinite non-Abelian group
Element a has infinite order
Inverses of generators:
- a^-1 = c²bc²
- b^-1 = acd
- c^-1 = cd
- d^-1 = c²
Reduced group presentation: ⟨a, b | aabab^-1abab^-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 = bcca
Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = 0, c < d; deg(b) = deg(a) = 1, b < a
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:ababbaabba=1 cd/ba ba=c,bcca=d morph:2/0,4/0
dc=cd
ccd=1
db=cbcc
cccb=bd
da=accc
cca=acdd
ba=c
cbca=bcac
accb=d
cab=abc
cacb=acbc
abca=cac

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

2 total

Σ	#	Presentation	Mapping
10	1532	⟨a, b \| abbaababba=1⟩	φ(a) = a, φ(b) = ccbccab
10	1533	⟨a, b \| abbaabbaab=1⟩	φ(a) = a, φ(b) = ccbccab