Certificate for #448 ⟨a, b | aababa=ab⟩

Back:⟨a, b | aababa=ab⟩

Completion settings:

[1] aababa=ab

Axiom: aababa=ab.

Referenced by [3].

[2] ab=c

Axiom: ab=c.

Defines rule #3.

Referenced by [3], [4], [5].

[3] aababa=c

Simplify [1] aababa=ab.

Reduce RHS:

[2](ab)
⇒ c

Referenced by [4].

[4] acca=c

Overlap of [3] aababa=c with [2] ab=c:

a ababa ab

Critical pair: acaba=c.

Reduce LHS:

[2]ac(ab)a
⇒ acca

Defines rule #1.

Referenced by [5], [6].

[5] cb=accc

Overlap of [4] acca=c with [2] ab=c:

acc a ab

Critical pair: accc=cb.

Flip LHS and RHS.

Defines rule #4.

[6] ccca=accc

Overlap of [4] acca=c with [4] acca=c:

acc a acca

Critical pair: accc=ccca.

Flip LHS and RHS.

Defines rule #2.