Certificate for #16378 ⟨a, b | aba=ab, aaab=ab⟩

Back:⟨a, b | aba=ab, aaab=ab⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Referenced by [4].

[2] aaab=ab

Axiom: aaab=ab.

Referenced by [6].

[3] ab=c

Axiom: ab=c.

Defines rule #1.

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

[4] aba=c

Simplify [1] 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 [8].

[6] aaab=c

Simplify [2] aaab=ab.

Reduce RHS:

[3](ab)
⇒ c

Referenced by [7].

[7] aac=c

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

aa ab ab

Critical pair: aac=c.

Defines rule #4.

[8] 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.