#2982 ⟨a, b | aaabbbaaabb=1⟩

Properties

Sum of relation sides is 11
Infinite non-Abelian group
Element aba has infinite order
Inverses of generators:
- a^-1 = a²b⁵c
- b^-1 = b⁴c²
- c^-1 = b⁵c
- d^-1 = c
Reduced group presentation: ⟨a, b | aaabbaaabbb⟩
- 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 = bbbaaabb
Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = deg(d) = 1, a < d
Certificate: derivations of all rewriting rules from the defining relations.

# ab:aaabbbaaabb=1 bc/ad aaa=c,bbbaaabb=d magic:0
cb=bc
bbbbbcc=1
ca=ac
bbbbba=abbbbb
d=bbbbbc
aaa=c

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

4 total

Σ	#	Presentation	Mapping
11	3104	⟨a, b \| aabbaaabbba=1⟩	φ(a) = a, φ(b) = b
11	3138	⟨a, b \| aabbbaaabba=1⟩	φ(a) = a, φ(b) = b
11	3142	⟨a, b \| aabbbaabbba=1⟩	φ(a) = b, φ(b) = a
11	3296	⟨a, b \| abbbaaabbba=1⟩	φ(a) = b, φ(b) = a