Certificate for #16031 ⟨a, b | aaa=ab, bbaa=ba⟩

Back:⟨a, b | aaa=ab, bbaa=ba⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[2] bbaa=ba

Axiom: bbaa=ba.

Referenced by [3], [4], [5], [6], [7].

[3] aaaaaaa=aaaa

Overlap of [1] ab=aaa with [2] bbaa=ba:

a b bbaa

Critical pair: aba=aaabaa.

Reduce LHS:

[1](ab)a
⇒ aaaa

Reduce RHS:

[1]aa(ab)aa
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #1.

Referenced by [4].

[4] baaaaaa=baaa

Overlap of [2] bbaa=ba with [3] aaaaaaa=aaaa:

bb aa aaaaaaa

Critical pair: bbaaaa=baaaaaa.

Reduce LHS:

[2](bbaa)aa
⇒ baaa

Flip LHS and RHS.

Referenced by [5].

[5] baaaaa=baa

Overlap of [2] bbaa=ba with [4] baaaaaa=baaa:

b baa baaaaaa

Critical pair: bbaaa=baaaaa.

Reduce LHS:

[2](bbaa)a
⇒ baa

Flip LHS and RHS.

Referenced by [6].

[6] baaaa=ba

Overlap of [2] bbaa=ba with [5] baaaaa=baa:

b baa baaaaa

Critical pair: bbaa=baaaa.

Reduce LHS:

[2](bbaa)
⇒ ba

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[7] bba=baaa

Overlap of [2] bbaa=ba with [6] baaaa=ba:

b baa baaaa

Critical pair: bba=baaa.

Defines rule #4.