Certificate for #13183 ⟨a, b | abb=aaa, bab=ab⟩

Back:⟨a, b | abb=aaa, bab=ab⟩

Completion settings:

[1] abb=aaa

Axiom: abb=aaa.

Defines rule #1.

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

[2] bab=ab

Axiom: bab=ab.

Defines rule #2.

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

[3] baab=aab

Overlap of [2] bab=ab with [2] bab=ab:

ba b bab

Critical pair: baab=abab.

Reduce RHS:

[2]a(bab)
⇒ aab

Defines rule #4.

[4] aaaab=aab

Overlap of [1] abb=aaa with [2] bab=ab:

ab b bab

Critical pair: abab=aaaab.

Reduce LHS:

[2]a(bab)
⇒ aab

Flip LHS and RHS.

Defines rule #5.

[5] baaa=aaa

Overlap of [2] bab=ab with [1] abb=aaa:

b ab abb

Critical pair: baaa=abb.

Reduce RHS:

[1](abb)
⇒ aaa

Defines rule #3.

Referenced by [6].

[6] aaaaaa=aaaa

Overlap of [1] abb=aaa with [5] baaa=aaa:

ab b baaa

Critical pair: abaaa=aaaaaa.

Reduce LHS:

[5]a(baaa)
⇒ aaaa

Flip LHS and RHS.

Defines rule #6.