#3479 ⟨a, b, c | bb=aa, aac=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bcb²c = b² and b ⋅ b = b², however bcb²c ≠ b

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(c) = deg(b) = 0, c < b; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:bb=aa,aac=a cb/a - -
bbbbc=bbcbb
bbcbbc=bb
a=bbc

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

2 total

Σ	#	Presentation	Mapping
8	3480	⟨a, b, c \| bb=aa, aac=b⟩	φ(a) = b, φ(b) = bbc, φ(c) = c
8	5248	⟨a, b, c \| aa=b, bcbc=b⟩	φ(a) = b, φ(b) = bb, φ(c) = c