Certificate for #4158 ⟨a, b | abb=aab, baa=a⟩

Back:⟨a, b | abb=aab, baa=a⟩

Completion settings:

[1] abb=aab

Axiom: abb=aab.

Defines rule #3.

Referenced by [3].

[2] baa=a

Axiom: baa=a.

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

[3] aba=aaa

Overlap of [1] abb=aab with [2] baa=a:

ab b baa

Critical pair: aba=aabaa.

Reduce RHS:

[2]aa(baa)
⇒ aaa

Referenced by [4].

[4] aaaa=aa

Overlap of [3] aba=aaa with [2] baa=a:

a ba baa

Critical pair: aa=aaaa.

Flip LHS and RHS.

Referenced by [5].

[5] aaa=a

Overlap of [2] baa=a with [4] aaaa=aa:

b aa aaaa

Critical pair: baa=aaa.

Reduce LHS:

[2](baa)
⇒ a

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

[6] ba=aa

Overlap of [2] baa=a with [5] aaa=a:

b aa aaa

Critical pair: ba=aa.

Defines rule #1.