#2875 ⟨a, b | aaaabbaabba=1⟩

Properties

Sum of relation sides is 11
Infinite non-Abelian group
Element ada has infinite order
Inverses of generators:
- a^-1 = d²a²
- b^-1 = bcda²
- c^-1 = d²
- d^-1 = cd
Reduced group presentation: ⟨a, b | aaaaabbaabb⟩
- Isomorphism: φ(a) = a, φ(b) = b

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

# ab:aaaabbaabba=1 cda/b aaa=c,aabb=d morph:3/0,4/0
dc=cd
ac=ca
cdd=1
add=dda
aaa=c
adb=cbddad
aab=dbcdaa
bb=ddad

1 unique, 1 total

Σ	#	Presentation	Properties
11	4866	⟨a, b \| abbaabba=bbb⟩	Can Inf

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

4 total

Σ	#	Presentation	Mapping
11	2964	⟨a, b \| aaabbaabbaa=1⟩	φ(a) = a, φ(b) = b
11	3097	⟨a, b \| aabbaaaaabb=1⟩	φ(a) = a, φ(b) = b
11	3270	⟨a, b \| abbaaaaabba=1⟩	φ(a) = a, φ(b) = b
11	3283	⟨a, b \| abbaabbbbba=1⟩	φ(a) = b, φ(b) = a