#4653 ⟨a, b | aaab=a, abaa=a⟩

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 a is not injective:
- a ⋅ ac = a and a ⋅ 1 = a, however ac ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- ac ⋅ c = c and 1 ⋅ c = c, however ac ≠ 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:aaab=a,abaa=a ac/b ab=c morph:2/0
ca=ac
aac=a
acc=c
ab=c
cb=ccc

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

3 total

Σ	#	Presentation	Mapping
11	12934	⟨a, b \| aba=aab, aaab=a⟩	φ(a) = a, φ(b) = b
11	12936	⟨a, b \| aba=aab, aaba=a⟩	φ(a) = a, φ(b) = b
11	12940	⟨a, b \| aba=aab, abaa=a⟩	φ(a) = a, φ(b) = b