#12635 ⟨a, b | babb=ab, bbbb=b⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b³ = b and b ⋅ 1 = b, however b³ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b³ ⋅ b = b and 1 ⋅ b = b, however b³ ≠ 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 = ab
Reduction order:
- Right-to-left recursive path with deg(b) = 0; deg(c) = deg(a) = 1, c < a
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:babb=ab,bbbb=b reversed:b/ca ab=c morph:2/0
bbbb=b
bbbc=c
cb=bbc
ab=c
ac=bcc