#2991 ⟨a, b | aaabbbabbba=1⟩

Properties

Sum of relation sides is 11
Infinite non-Abelian group
Element a has infinite order
Inverses of generators:
- a^-1 = da²
- b^-1 = b²a⁴ca
- c^-1 = a⁴ca
- d^-1 = a³
Reduced group presentation: ⟨a, b | aaaabbbabbb⟩
- 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 = bbb
2. d = acac
Reduction order:
- Right-to-left recursive path with deg(a) = deg(d) = 0, a < d; deg(c) = deg(b) = 1, c < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aaabbbabbba=1 reversed:ad/cb bbb=c,acac=d morph:3/0,4/0
ad=da
daaa=1
cd=dc
caaa=aaac
cac=ddaa
cb=bc
cab=ddaabaaaaca
bbb=c

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

4 total

Σ	#	Presentation	Mapping
11	2992	⟨a, b \| aaabbbbaaab=1⟩	φ(a) = b, φ(b) = a
11	3028	⟨a, b \| aabaaabbbba=1⟩	φ(a) = b, φ(b) = a
11	3149	⟨a, b \| aabbbabbbaa=1⟩	φ(a) = a, φ(b) = b
11	3153	⟨a, b \| aabbbbaaaba=1⟩	φ(a) = b, φ(b) = a