#3186 ⟨a, b, c | ba=ab, abca=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bc = bcb and b ⋅ cb = bcb, however bc ≠ cb
Not right cancellative, because right multiplication by c is not injective:
- ca²b ⋅ c = c and 1 ⋅ c = c, however ca²b ≠ 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

# abc:ba=ab,abca=1 acb - -
ba=ab
bca=abc
bbc=bcb
aabc=1

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

1 total

Σ	#	Presentation	Mapping
8	3187	⟨a, b, c \| ba=ab, abcb=1⟩	φ(a) = b, φ(b) = a, φ(c) = c