Certificate for #5317 ⟨a, b | abaabab=baba⟩

Back:⟨a, b | abaabab=baba⟩

Completion settings:

[1] abaabab=baba

Axiom: abaabab=baba.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #3.

Referenced by [3], [4], [5], [6].

[3] abaabab=cc

Simplify [1] abaabab=baba.

Reduce RHS:

[2](ba)ba
[2]⇒ c(ba)
⇒ cc

Referenced by [4].

[4] acacb=cc

Overlap of [3] abaabab=cc with [2] ba=c:

a baabab ba

Critical pair: acabab=cc.

Reduce LHS:

[2]aca(ba)b
⇒ acacb

Defines rule #2.

Referenced by [5], [6].

[5] bcc=ccacb

Overlap of [2] ba=c with [4] acacb=cc:

b a acacb

Critical pair: bcc=ccacb.

Defines rule #4.

[6] acacc=cca

Overlap of [4] acacb=cc with [2] ba=c:

acac b ba

Critical pair: acacc=cca.

Defines rule #1.