Certificate for #16035 ⟨a, b | aaa=ab, bbab=ba⟩

Back:⟨a, b | aaa=ab, bbab=ba⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3].

[2] bbaaa=ba

Axiom: bbab=ba.

Reduce LHS:

[1]bb(ab)
⇒ bbaaa

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

[3] aaaaaaaa=aaaa

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

a b bbaaa

Critical pair: aba=aaabaaa.

Reduce LHS:

[1](ab)a
⇒ aaaa

Reduce RHS:

[1]aa(ab)aaa
⇒ aaaaaaaa

Flip LHS and RHS.

Defines rule #1.

Referenced by [4].

[4] baaaaaa=baa

Overlap of [2] bbaaa=ba with [3] aaaaaaaa=aaaa:

bb aaa aaaaaaaa

Critical pair: bbaaaa=baaaaaa.

Reduce LHS:

[2](bbaaa)a
⇒ baa

Flip LHS and RHS.

Referenced by [5].

[5] bbaa=baaaa

Overlap of [2] bbaaa=ba with [4] baaaaaa=baa:

b baaa baaaaaa

Critical pair: bbaa=baaaa.

Referenced by [6].

[6] baaaaa=ba

Overlap of [2] bbaaa=ba with [5] bbaa=baaaa:

bbaaa bbaa

Critical pair: baaaaa=ba.

Defines rule #2.

Referenced by [7].

[7] bba=baaa

Overlap of [2] bbaaa=ba with [6] baaaaa=ba:

b baaa baaaaa

Critical pair: bba=baaa.

Defines rule #4.