Certificate for #20217 ⟨a, b | aba=a, abba=abb⟩

Back:⟨a, b | aba=a, abba=abb⟩

Completion settings:

[1] aba=a

Axiom: aba=a.

Referenced by [4].

[2] abba=abb

Axiom: abba=abb.

Referenced by [5].

[3] ab=c

Axiom: ab=c.

Defines rule #1.

Referenced by [4], [5], [6], [7], [8].

[4] ca=a

Overlap of [1] aba=a with [3] ab=c:

aba ab

Critical pair: ca=a.

Defines rule #2.

Referenced by [7].

[5] abba=cb

Simplify [2] abba=abb.

Reduce RHS:

[3](ab)b
⇒ cb

Referenced by [6].

[6] cba=cb

Overlap of [5] abba=cb with [3] ab=c:

abba ab

Critical pair: cba=cb.

Defines rule #4.

Referenced by [8].

[7] cc=c

Overlap of [4] ca=a with [3] ab=c:

c a ab

Critical pair: cc=ab.

Reduce RHS:

[3](ab)
⇒ c

Defines rule #3.

[8] cbb=cbc

Overlap of [6] cba=cb with [3] ab=c:

cb a ab

Critical pair: cbc=cbb.

Flip LHS and RHS.

Defines rule #5.