Certificate for #16033 ⟨a, b | aaa=ab, bbab=aa⟩

Back:⟨a, b | aaa=ab, bbab=aa⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3].

[2] bbaaa=aa

Axiom: bbab=aa.

Reduce LHS:

[1]bb(ab)
⇒ bbaaa

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

[3] aaaaaaaa=aaa

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

a b bbaaa

Critical pair: aaa=aaabaaa.

Reduce RHS:

[1]aa(ab)aaa
⇒ aaaaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] aaaaaaa=aa

Overlap of [2] bbaaa=aa with [3] aaaaaaaa=aaa:

bb aaa aaaaaaaa

Critical pair: bbaaa=aaaaaaa.

Reduce LHS:

[2](bbaaa)
⇒ aa

Flip LHS and RHS.

Defines rule #1.

Referenced by [5].

[5] bbaa=aaaaaa

Overlap of [2] bbaaa=aa with [4] aaaaaaa=aa:

bb aaa aaaaaaa

Critical pair: bbaa=aaaaaa.

Defines rule #3.