Certificate for #16032 ⟨a, b | aaa=ab, bbaa=bb⟩

Back:⟨a, b | aaa=ab, bbaa=bb⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[2] bbaa=bb

Axiom: bbaa=bb.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaaaa=aaaaa

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

a b bbaa

Critical pair: abb=aaabaa.

Reduce LHS:

[1](ab)b
[1]⇒ aa(ab)
⇒ aaaaa

Reduce RHS:

[1]aa(ab)aa
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #1.

[4] bbb=bb

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

bba a ab

Critical pair: bbaaaa=bbb.

Reduce LHS:

[2](bbaa)aa
[2]⇒ (bbaa)
⇒ bb

Flip LHS and RHS.

Defines rule #4.