#5650 ⟨a, b | aabaab=aabab⟩

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 ⋅ aba²b = a(ab)² and a ⋅ (ab)² = a(ab)², however aba²b ≠ (ab)²
Not right cancellative, because right multiplication by b is not injective:
- a²ba² ⋅ b = a(ab)² and a²ba ⋅ b = a(ab)², however a²ba² ≠ a²ba

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 = aabab
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.

# ab:aabaab=aabab ac/b aabab=c magic:0
cab=aabc
caab=aabc
aabab=c
aabaab=c