Certificate for #112 ⟨a, b | abba=ab⟩

Back:⟨a, b | abba=ab⟩

Completion settings:

[1] abba=ab

Axiom: abba=ab.

Referenced by [3].

[2] abb=c

Axiom: abb=c.

Referenced by [3], [4].

[3] ab=ca

Overlap of [1] abba=ab with [2] abb=c:

abba abb

Critical pair: ca=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] cca=c

Overlap of [2] abb=c with [3] ab=ca:

abb ab

Critical pair: cab=c.

Reduce LHS:

[3]c(ab)
⇒ cca

Defines rule #3.

Referenced by [5].

[5] cb=cc

Overlap of [4] cca=c with [3] ab=ca:

cc a ab

Critical pair: ccca=cb.

Reduce LHS:

[4]c(cca)
⇒ cc

Flip LHS and RHS.

Defines rule #1.