#5693 ⟨a, b, c | aa=b, abc=cb⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaba^-1a^-1b^-1⟩
- Embedding: φ(a) = a, φ(b) = aa, φ(c) = b

Format:	Pretty Plain
Word:
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Strategy:	Leftmost Rightmost
Result:	1 1

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

#	Rule	Proof
1.	a³c ⇒ ca²	[2]
2.	b ⇒ a²	[1]

# abc:aa=b,abc=cb ac/b - -
aaac=caa
b=aa

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

1 total

Σ	#	Presentation	Mapping
8	5729	⟨a, b, c \| aa=b, bac=cb⟩	φ(a) = a, φ(b) = aa, φ(c) = c