Certificate for #13129 ⟨a, b | aab=aaa, baa=ab⟩

Back:⟨a, b | aab=aaa, baa=ab⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Referenced by [3].

[2] ab=baa

Axiom: baa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] baaaa=aaa

Overlap of [1] aab=aaa with [2] ab=baa:

a ab ab

Critical pair: abaa=aaa.

Reduce LHS:

[2](ab)aa
⇒ baaaa

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

[4] aaaaa=aaaa

Overlap of [2] ab=baa with [3] baaaa=aaa:

a b baaaa

Critical pair: aaaa=baaaaaa.

Reduce RHS:

[3](baaaa)aa
⇒ aaaaa

Flip LHS and RHS.

Referenced by [5].

[5] aaaa=aaa

Overlap of [3] baaaa=aaa with [4] aaaaa=aaaa:

b aaaa aaaaa

Critical pair: baaaa=aaaa.

Reduce LHS:

[3](baaaa)
⇒ aaa

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

[6] baaa=aaa

Overlap of [3] baaaa=aaa with [5] aaaa=aaa:

b aaaa aaaa

Critical pair: baaa=aaa.

Defines rule #2.