#2504 ⟨a, b | aababa=baab⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabab^-1abb⟩
- Embedding: φ(a) = aba, φ(b) = a^-1b^-1a^-1b^-1a^-1

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 = baab
Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(c) = deg(b) = 1, c < b
Certificate: derivations of all rewriting rules from the defining relations.

# ab:aababa=baab a/cb baab=c magic:0
bc=caba
baac=caab
aabac=cab
baab=c
aababa=c

5 unique, 10 total

Σ	#	Presentation	Properties	φ
8	400	⟨a, b \| abaabba=b⟩	Can Inf
8	534	⟨a, b \| aabba=bab⟩	Can Inf
10	1419	⟨a, b \| aababaabba=1⟩	Grp Inf	5
10	1758	⟨a, b \| abaaababa=b⟩	Can Inf
10	2340	⟨a, b \| ababbba=bab⟩	Can Inf