#1587 ⟨a, b | aaaababaa=a⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a³c = a and a ⋅ 1 = a, however a³c ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- a³c ⋅ c = c and 1 ⋅ c = c, however a³c ≠ 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

Auxiliary generators:
1. c = ababa
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.
Morphocompletion: how the auxiliary generators were found.

# ab:aaaababaa=a ac/b ababa=c morph:5/0
ca=ac
aaaac=a
aaacc=c
cba=abc
cbc=abaaccc
aaaaaba=abaaaaa
aaaaabc=aba
ababa=c
ababc=aaccc

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

2 total

Σ	#	Presentation	Mapping
10	1623	⟨a, b \| aaababaaa=a⟩	φ(a) = a, φ(b) = b
10	1749	⟨a, b \| abaaaaaba=a⟩	φ(a) = a, φ(b) = b