Certificate for #13210 ⟨a, b | abb=aba, bab=aa⟩

Completion settings:

Reduction order:
- Left-to-right shortlex with a < b

[1] abb=aba

Axiom: abb=aba.

Defines rule #2.

Referenced by [4], [5].

[2] bab=aa

Axiom: bab=aa.

Defines rule #3.

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

[3] baaa=aaab

Overlap of [2] bab=aa with [2] bab=aa:

ba b bab

Critical pair: baaa=aaab.

Referenced by [7].

[4] abaab=abaa

Overlap of [1] abb=aba with [2] bab=aa:

ab b bab

Critical pair: abaa=abaab.

Flip LHS and RHS.

Referenced by [8].

[5] aab=aaa

Overlap of [2] bab=aa with [1] abb=aba:

b ab abb

Critical pair: baba=aab.

Reduce LHS:

[2]	(bab)a
	⇒ aaa

Flip LHS and RHS.

Defines rule #1.

Referenced by [6], [7], [8].

[6] aaaaa=aaaa

Overlap of [5] aab=aaa with [2] bab=aa:

aa b bab

Critical pair: aaaa=aaaab.

Reduce RHS:

[5]	aa(aab)
	⇒ aaaaa

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

[7] baaa=aaaa

Simplify [3] baaa=aaab.

Reduce RHS:

[5]	a(aab)
	⇒ aaaa

Defines rule #5.

Referenced by [8].

[8] abaa=aaaa

Simplify [4] abaab=abaa.

Reduce LHS:

[5]	ab(aab)
[7]	⇒ a(baaa)
[6]	⇒ (aaaaa)
	⇒ aaaa

Flip LHS and RHS.

Defines rule #4.