Certificate for #16036 ⟨a, b | aaa=ab, bbab=bb⟩

Back:⟨a, b | aaa=ab, bbab=bb⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [2], [3], [4].

[2] bbaaa=bb

Axiom: bbab=bb.

Reduce LHS:

[1]bb(ab)
⇒ bbaaa

Defines rule #3.

Referenced by [3], [4].

[3] aaaaaaaa=aaaaa

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

a b bbaaa

Critical pair: abb=aaabaaa.

Reduce LHS:

[1](ab)b
[1]⇒ aa(ab)
⇒ aaaaa

Reduce RHS:

[1]aa(ab)aaa
⇒ aaaaaaaa

Flip LHS and RHS.

Defines rule #1.

[4] bbb=bbaa

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

bbaa a ab

Critical pair: bbaaaaa=bbb.

Reduce LHS:

[2](bbaaa)aa
⇒ bbaa

Flip LHS and RHS.

Defines rule #4.