#6682 ⟨a, b, c | aa=1, abcba=b⟩

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 ⋅ (cab)² = b and b ⋅ 1 = b, however (cab)² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- (bca)² ⋅ b = b and 1 ⋅ b = b, however (bca)² ≠ 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:aa=1,abcba=b bc/a - -
ba=abcb
bcabcb=ab
aa=1
bcabcab=b

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

2 total

Σ	#	Presentation	Mapping
8	7182	⟨a, b, c \| aa=1, abcb=ba⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7680	⟨a, b, c \| aa=1, bcb=aba⟩	φ(a) = a, φ(b) = b, φ(c) = c