#289 ⟨a, b, c | aab=a, bcb=1⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ab = a and a ⋅ 1 = a, however ab ≠ 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(a) = deg(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aab=a,bcb=1 ab/c - -
aab=a
cbb=1
ac=aaa
bc=cb

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

2 total

Σ	#	Presentation	Mapping
8	1919	⟨a, b, c \| abc=aa, bcb=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	1926	⟨a, b, c \| abc=aa, cbc=1⟩	φ(a) = a, φ(b) = c, φ(c) = b