#333 ⟨a, b | ababbaba=1⟩

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element b has infinite order
Inverses of generators:
- a^-1 = ad²
- b^-1 = abdc
- c^-1 = d²
- d^-1 = dc
Reduced group presentation: ⟨a, b | aabaab^-1⟩
- Isomorphism: φ(a) = b, φ(b) = b^-1a

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

# ab:ababbaba=1 dc/ab aa=c,bab=d morph:2/0,3/0
cd=dc
ddc=1
ca=ac
dda=add
aa=c
ba=dabdc
bda=adb
bdcb=add

1 unique, 1 total

Σ	#	Presentation	Properties
6	83	⟨a, b \| aabaa=b⟩	Can Inf

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

1 total

Σ	#	Presentation	Mapping
8	337	⟨a, b \| abbabaab=1⟩	φ(a) = a, φ(b) = addab