Certificate for #5374 ⟨a, b | aab=ab, aba=ab⟩

Back:⟨a, b | aab=ab, aba=ab⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Referenced by [4].

[2] aba=ab

Axiom: aba=ab.

Referenced by [6].

[3] ab=c

Axiom: ab=c.

Defines rule #2.

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

[4] aab=c

Simplify [1] aab=ab.

Reduce RHS:

[3](ab)
⇒ c

Referenced by [5].

[5] ac=c

Overlap of [4] aab=c with [3] ab=c:

a ab ab

Critical pair: ac=c.

Defines rule #1.

[6] aba=c

Simplify [2] aba=ab.

Reduce RHS:

[3](ab)
⇒ c

Referenced by [7].

[7] ca=c

Overlap of [6] aba=c with [3] ab=c:

aba ab

Critical pair: ca=c.

Defines rule #3.

Referenced by [8].

[8] cb=cc

Overlap of [7] ca=c with [3] ab=c:

c a ab

Critical pair: cc=cb.

Flip LHS and RHS.

Defines rule #4.