Certificate for #5356 ⟨a, b | aab=aa, aba=bb⟩

Completion settings:

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

[1] aab=aa

Axiom: aab=aa.

Defines rule #3.

Referenced by [3], [5], [6], [7].

[2] bb=aba

Axiom: aba=bb.

Flip LHS and RHS.

Defines rule #4.

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

[3] aaaa=aa

Overlap of [1] aab=aa with [2] bb=aba:

aa b bb

Critical pair: aaaba=aab.

Reduce LHS:

[1]	a(aab)a
	⇒ aaaa

Reduce RHS:

[1]	(aab)
	⇒ aa

Defines rule #1.

Referenced by [6], [7].

[4] abab=baba

Overlap of [2] bb=aba with [2] bb=aba:

b b bb

Critical pair: baba=abab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [5].

[5] babaa=aaa

Overlap of [1] aab=aa with [4] abab=baba:

a ab abab

Critical pair: ababa=aaab.

Reduce LHS:

[4]	(abab)a
	⇒ babaa

Reduce RHS:

[1]	a(aab)
	⇒ aaa

Referenced by [6].

[6] abaa=baaa

Overlap of [2] bb=aba with [5] babaa=aaa:

b b babaa

Critical pair: baaa=abaabaa.

Reduce RHS:

[1]	ab(aab)aa
[3]	⇒ ab(aaaa)
	⇒ abaa

Flip LHS and RHS.

Referenced by [7].

[7] baa=aa

Overlap of [1] aab=aa with [6] abaa=baaa:

a ab abaa

Critical pair: abaaa=aaaa.

Reduce LHS:

[6]	(abaa)a
[3]	⇒ b(aaaa)
	⇒ baa

Reduce RHS:

[3]	(aaaa)
	⇒ aa

Defines rule #2.