Certificate for #4151 ⟨a, b | abb=aaa, baa=b⟩

Back:⟨a, b | abb=aaa, baa=b⟩

Completion settings:

[1] abb=aaa

Axiom: abb=aaa.

Defines rule #1.

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

[2] baa=b

Axiom: baa=b.

Defines rule #2.

Referenced by [3], [4].

[3] aaaaa=aaa

Overlap of [1] abb=aaa with [2] baa=b:

ab b baa

Critical pair: abb=aaaaa.

Reduce LHS:

[1](abb)
⇒ aaa

Flip LHS and RHS.

Defines rule #5.

[4] bbb=b

Overlap of [2] baa=b with [1] abb=aaa:

ba a abb

Critical pair: baaaa=bbb.

Reduce LHS:

[2](baa)aa
[2]⇒ (baa)
⇒ b

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] aaab=ab

Overlap of [1] abb=aaa with [4] bbb=b:

a bb bbb

Critical pair: ab=aaab.

Flip LHS and RHS.

Defines rule #4.