Certificate for #16162 ⟨a, b | aab=ab, abaa=ab⟩

Back:⟨a, b | aab=ab, abaa=ab⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Referenced by [4].

[2] abaa=ab

Axiom: abaa=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.

Referenced by [8].

[6] abaa=c

Simplify [2] abaa=ab.

Reduce RHS:

[3](ab)
⇒ c

Referenced by [7].

[7] caa=c

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

abaa ab

Critical pair: caa=c.

Defines rule #4.

Referenced by [8].

[8] cb=cc

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

ca a ab

Critical pair: cac=cb.

Reduce LHS:

[5]c(ac)
⇒ cc

Flip LHS and RHS.

Defines rule #3.