Certificate for #5138 ⟨a, b | aabaaba=abab⟩

Back:⟨a, b | aabaaba=abab⟩

Completion settings:

[1] aabaaba=abab

Axiom: aabaaba=abab.

Referenced by [3].

[2] ab=c

Axiom: ab=c.

Defines rule #3.

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

[3] aabaaba=cc

Simplify [1] aabaaba=abab.

Reduce RHS:

[2](ab)ab
[2]⇒ c(ab)
⇒ cc

Referenced by [4].

[4] acaca=cc

Overlap of [3] aabaaba=cc with [2] ab=c:

a abaaba ab

Critical pair: acaaba=cc.

Reduce LHS:

[2]aca(ab)a
⇒ acaca

Defines rule #2.

Referenced by [5], [6].

[5] ccb=acacc

Overlap of [4] acaca=cc with [2] ab=c:

acac a ab

Critical pair: acacc=ccb.

Flip LHS and RHS.

Defines rule #4.

[6] ccca=accc

Overlap of [4] acaca=cc with [4] acaca=cc:

ac aca acaca

Critical pair: accc=ccca.

Flip LHS and RHS.

Defines rule #1.