Certificate for #1807 ⟨a, b, c | aba=ab, abc=1⟩

Back:⟨a, b, c | aba=ab, abc=1⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Referenced by [4].

[2] abc=1

Axiom: abc=1.

Referenced by [6].

[3] ab=d

Axiom: ab=d.

Defines rule #1.

Referenced by [4], [5], [6], [7].

[4] aba=d

Simplify [1] aba=ab.

Reduce RHS:

[3](ab)
⇒ d

Referenced by [5].

[5] da=d

Overlap of [4] aba=d with [3] ab=d:

aba ab

Critical pair: da=d.

Defines rule #2.

Referenced by [7].

[6] dc=1

Overlap of [2] abc=1 with [3] ab=d:

abc ab

Critical pair: dc=1.

Defines rule #4.

[7] db=dd

Overlap of [5] da=d with [3] ab=d:

d a ab

Critical pair: dd=db.

Flip LHS and RHS.

Defines rule #3.