#2956 ⟨a, b | aaabbaaaabb=1⟩

Properties

Sum of relation sides is 11
Infinite non-Abelian group
Element c has infinite order
Inverses of generators:
- a^-1 = a³d
- b^-1 = a³b²d⁶bc⁷
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaabbaaabb⟩
- 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 = aaaa
2. d = bbaaabb
Reduction order:
- Left-to-right recursive path with deg(d) = 0; deg(c) = 1; deg(a) = deg(b) = 2, a < b
Certificate: derivations of all rewriting rules from the defining relations.

# ab:aaabbaaaabb=1 d/c/ab aaaa=c,bbaaabb=d magic:0
cd=1
dc=1
da=ad
ca=ac
dddddddb=bddddddd
cb=ddddddbccccccc
ba=addbcc
dbb=bbd
aaaa=c
bbbb=add

1 unique, 1 total

Σ	#	Presentation	Properties
11	3826	⟨a, b \| abbbaabbba=b⟩	Can Inf

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

4 total

Σ	#	Presentation	Mapping
11	2959	⟨a, b \| aaabbaaabba=1⟩	φ(a) = a, φ(b) = b
11	3099	⟨a, b \| aabbaaaabba=1⟩	φ(a) = a, φ(b) = b
11	3102	⟨a, b \| aabbaaabbaa=1⟩	φ(a) = a, φ(b) = b
11	3298	⟨a, b \| abbbaabbbba=1⟩	φ(a) = b, φ(b) = a