#2831 ⟨a, b | aaaaabbabba=1⟩

Properties

Sum of relation sides is 11
Infinite non-Abelian group
Element a³ca has infinite order
Inverses of generators:
- a^-1 = c²a⁴
- b^-1 = bdac
- c^-1 = dc
- d^-1 = c²
Reduced group presentation: ⟨a, b | aaaaaabbabb⟩
- 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 = bba
2. d = aaaaa
Reduction order:
- Left-to-right recursive path with deg(d) = deg(c) = deg(a) = 0, d < c < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aaaaabbabba=1 dca/b bba=c,aaaaa=d morph:3/0,5/0
cd=dc
ad=da
dcc=1
acc=cca
aaaaa=d
acb=ccbdac
aaaab=ddcbcccaaaa
bb=cccaaaa

1 unique, 1 total

Σ	#	Presentation	Properties
11	5860	⟨a, b \| abaaba=bbbbb⟩	Can Inf

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

4 total

Σ	#	Presentation	Mapping
11	2881	⟨a, b \| aaaabbabbaa=1⟩	φ(a) = a, φ(b) = b
11	2973	⟨a, b \| aaabbabbaaa=1⟩	φ(a) = a, φ(b) = b
11	3164	⟨a, b \| aabbbbbbaab=1⟩	φ(a) = b, φ(b) = a
11	3226	⟨a, b \| abaabbbbbba=1⟩	φ(a) = b, φ(b) = a