#4671 ⟨a, b | aaab=a, bbab=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a⁶ = a and a ⋅ 1 = a, however a⁶ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a⁶ ⋅ a = a and 1 ⋅ a = a, however a⁶ ≠ 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

# ab:aaab=a,bbab=a a/b - -
aaaaaaa=a
ab=aaaaa
bba=aaa

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

2 total

Σ	#	Presentation	Mapping
10	4714	⟨a, b \| aaba=a, bbab=a⟩	φ(a) = a, φ(b) = b
11	12990	⟨a, b \| abb=aaa, bbab=a⟩	φ(a) = a, φ(b) = b

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

3 total

Σ	#	Presentation	Mapping
10	4710	⟨a, b \| aaba=a, babb=a⟩	φ(a) = a, φ(b) = b
11	12980	⟨a, b \| abb=aaa, baaa=a⟩	φ(a) = a, φ(b) = b
11	12986	⟨a, b \| abb=aaa, babb=a⟩	φ(a) = a, φ(b) = b