Certificate for #5299 ⟨a, b | aaa=aa, aba=ab⟩

Back:⟨a, b | aaa=aa, aba=ab⟩

Completion settings:

[1] aaa=aa

Axiom: aaa=aa.

Defines rule #4.

Referenced by [7].

[2] aba=ab

Axiom: aba=ab.

Referenced by [4].

[3] ab=c

Axiom: ab=c.

Defines rule #1.

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

[4] aba=c

Simplify [2] aba=ab.

Reduce RHS:

[3](ab)
⇒ c

Referenced by [5].

[5] ca=c

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

aba ab

Critical pair: ca=c.

Defines rule #2.

Referenced by [6].

[6] cb=cc

Overlap of [5] ca=c with [3] ab=c:

c a ab

Critical pair: cc=cb.

Flip LHS and RHS.

Defines rule #3.

[7] aac=ac

Overlap of [1] aaa=aa with [3] ab=c:

aa a ab

Critical pair: aac=aab.

Reduce RHS:

[3]a(ab)
⇒ ac

Defines rule #5.