Certificate for #5421 ⟨a, b | aba=bb, bab=aa⟩

Completion settings:

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

[1] bb=aba

Axiom: aba=bb.

Flip LHS and RHS.

Defines rule #5.

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

[2] bab=aa

Axiom: bab=aa.

Defines rule #6.

Referenced by [3], [4], [5], [8].

[3] abaab=baa

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

b b bab

Critical pair: baa=abaab.

Flip LHS and RHS.

Referenced by [7].

[4] baaba=aab

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

ba b bb

Critical pair: baaba=aab.

Referenced by [6], [9].

[5] aaab=baaa

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

ba b bab

Critical pair: baaa=aaab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [7].

[6] baab=aabaaaaa

Overlap of [1] bb=aba with [4] baaba=aab:

b b baaba

Critical pair: baab=abaaaba.

Reduce RHS:

[5]	ab(aaab)a
[1]	⇒ a(bb)aaaa
	⇒ aabaaaaa

Defines rule #7.

Referenced by [7], [9].

[7] baaaaaaaa=baa

Simplify [3] abaab=baa.

Reduce LHS:

[6]	a(baab)
[5]	⇒ (aaab)aaaaa
	⇒ baaaaaaaa

Defines rule #2.

Referenced by [8].

[8] aaaaaaaaaa=aaaa

Overlap of [2] bab=aa with [7] baaaaaaaa=baa:

ba b baaaaaaaa

Critical pair: babaa=aaaaaaaaaa.

Reduce LHS:

[2]	(bab)aa
	⇒ aaaa

Flip LHS and RHS.

Defines rule #1.

[9] aabaaaaaa=aab

Overlap of [4] baaba=aab with [6] baab=aabaaaaa:

baaba baab

Critical pair: aabaaaaaa=aab.

Defines rule #3.