Certificate for #16364 ⟨a, b | aba=aa, baab=ab⟩

Back:⟨a, b | aba=aa, baab=ab⟩

Completion settings:

[1] aba=aa

Axiom: aba=aa.

Defines rule #3.

Referenced by [3], [4].

[2] baab=ab

Axiom: baab=ab.

Referenced by [3], [7].

[3] baaa=aa

Overlap of [2] baab=ab with [1] aba=aa:

ba ab aba

Critical pair: baaa=aba.

Reduce RHS:

[1](aba)
⇒ aa

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

[4] aaaa=aaa

Overlap of [1] aba=aa with [3] baaa=aa:

a ba baaa

Critical pair: aaa=aaaa.

Flip LHS and RHS.

Referenced by [5].

[5] aaa=aa

Overlap of [3] baaa=aa with [4] aaaa=aaa:

b aaa aaaa

Critical pair: baaa=aaa.

Reduce LHS:

[3](baaa)
⇒ aa

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

[6] baa=aa

Overlap of [3] baaa=aa with [5] aaa=aa:

b aaa aaa

Critical pair: baa=aa.

Defines rule #4.

Referenced by [7], [8].

[7] aab=ab

Overlap of [2] baab=ab with [6] baa=aa:

baab baa

Critical pair: aab=ab.

Defines rule #2.

Referenced by [8].

[8] bab=ab

Overlap of [6] baa=aa with [7] aab=ab:

b aa aab

Critical pair: bab=aab.

Reduce RHS:

[7](aab)
⇒ ab

Defines rule #5.