#14339 ⟨a, b | aaaa=a, aabab=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element aca has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ c² = a and a ⋅ 1 = a, however c² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- c² ⋅ a = a and 1 ⋅ a = a, however c² ≠ 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:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aaaa=a,aabab=a ac/b ab=c morph:2/0
aaa=cc
acc=a
cca=a
ccc=c
ab=c
cb=caac