#2307 ⟨a, b | abaabab=aba⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ a = cbc and c ⋅ bc = cbc, however a ≠ bc

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

# ab:abaabab=aba bc/a abaa=c morph:4/1
ca=cbc
ccbabb=c
cbcba=ccbab
aba=cbab
cbaa=cbabc
cbabba=abcbab
cbacbabb=cba
cbabcba=cbacbab