Certificate for #19486 ⟨a, b | aab=a, bbabb=ba⟩

Completion settings:

Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1

[1] aab=a

Axiom: aab=a.

Referenced by [3], [4], [5], [6].

[2] bbabb=ba

Axiom: bbabb=ba.

Referenced by [3], [4], [6].

[3] ababb=aa

Overlap of [1] aab=a with [2] bbabb=ba:

aa b bbabb

Critical pair: aaba=ababb.

Reduce LHS:

[1]	(aab)a
	⇒ aa

Flip LHS and RHS.

Referenced by [5], [6].

[4] bbaba=bab

Overlap of [2] bbabb=ba with [2] bbabb=ba:

bba bb bbabb

Critical pair: bbaba=baabb.

Reduce RHS:

[1]	b(aab)b
	⇒ bab

Referenced by [7].

[5] ab=aaa

Overlap of [1] aab=a with [3] ababb=aa:

a ab ababb

Critical pair: aaa=aabb.

Reduce RHS:

[1]	(aab)b
	⇒ ab

Flip LHS and RHS.

Defines rule #2.

Referenced by [6], [7].

[6] aaaa=a

Overlap of [3] ababb=aa with [2] bbabb=ba:

aba bb bbabb

Critical pair: ababa=aaabb.

Reduce LHS:

[5]	(ab)aba
[1]	⇒ aa(aab)a
	⇒ aaaa

Reduce RHS:

[1]	a(aab)b
[1]	⇒ (aab)
	⇒ a

Defines rule #1.

Referenced by [7].

[7] bba=baaa

Simplify [4] bbaba=bab.

Reduce LHS:

[5]	bb(ab)a
[6]	⇒ bb(aaaa)
	⇒ bba

Reduce RHS:

[5]	b(ab)
	⇒ baaa

Defines rule #3.