#1044 ⟨a, b, c | ab=c, bcc=c⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by c is not injective:
- bc ⋅ c = c and 1 ⋅ c = c, however bc ≠ 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

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

# abc:ab=c,bcc=c bc/a - -
bcc=c
ab=c
ac=ccc

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

2 total

Σ	#	Presentation	Mapping
8	5564	⟨a, b, c \| ab=c, babc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6090	⟨a, b, c \| ab=c, bcc=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c