#3563 ⟨a, b | aabaababaa=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ (aba)²ba² = a and a ⋅ 1 = a, however (aba)²ba² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- (a²b)²aba ⋅ a = a and 1 ⋅ a = a, however (a²b)²aba ≠ 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 = aba
Reduction order:
- Right-to-left 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:aabaababaa=a reversed:ac/b aba=c morph:3/0
aacc=caca
cacc=a
aba=c
abc=cba
cbaa=accccba
cbca=cccccba
cbac=accccbc
cbcc=cccccbc

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

2 total

Σ	#	Presentation	Mapping
11	3582	⟨a, b \| aababaaaba=a⟩	φ(a) = a, φ(b) = b
11	3715	⟨a, b \| abaaabaaba=a⟩	φ(a) = a, φ(b) = b