Certificate for #1272 ⟨a, b | abbba=baab⟩

Back:⟨a, b | abbba=baab⟩

Completion settings:

[1] baab=abbba

Axiom: abbba=baab.

Flip LHS and RHS.

Referenced by [2], [3].

[2] abbba=c

Axiom: baab=c.

Reduce LHS:

[1](baab)
⇒ abbba

Defines rule #4.

Referenced by [3], [5], [6], [7].

[3] baab=c

Simplify [1] baab=abbba.

Reduce RHS:

[2](abbba)
⇒ c

Defines rule #5.

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

[4] caab=baac

Overlap of [3] baab=c with [3] baab=c:

baa b baab

Critical pair: baac=caab.

Flip LHS and RHS.

Defines rule #6.

[5] cbba=bac

Overlap of [3] baab=c with [2] abbba=c:

ba ab abbba

Critical pair: bac=cbba.

Flip LHS and RHS.

Defines rule #2.

[6] cab=abbc

Overlap of [2] abbba=c with [3] baab=c:

abb ba baab

Critical pair: abbc=cab.

Flip LHS and RHS.

Defines rule #1.

[7] cbbba=abbbc

Overlap of [2] abbba=c with [2] abbba=c:

abbb a abbba

Critical pair: abbbc=cbbba.

Flip LHS and RHS.

Defines rule #3.