#3563 ⟨a, b, c | ab=aa, cc=aa⟩

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 a is not injective:
- a ⋅ b = a² and a ⋅ a = a², however b ≠ a

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

Reduction order:
- Left-to-right recursive path with deg(a) = deg(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:ab=aa,cc=aa ab/c - -
ab=aa
aac=caa
cc=aa

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

2 total

Σ	#	Presentation	Mapping
8	3564	⟨a, b, c \| ab=aa, cc=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	3597	⟨a, b, c \| bb=aa, bc=aa⟩	φ(a) = c, φ(b) = a, φ(c) = b