#3728 ⟨a, b | abaabaaaab=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element d has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ bca²c = a and a ⋅ 1 = a, however bca²c ≠ 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 = aab
2. d = aaaa
Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(d) = deg(a) = deg(b) = 1, d < a < b
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abaabaaaab=a reversed:c/dab aab=c,aaaa=d morph:3/1,4/0
dc=ccccd
da=ad
ccaac=aa
db=aac
aaac=abcccd
acaac=abcd
aab=c
aaaa=d
abcaac=a