Certificate for #2208 ⟨a, b, c | aabc=1, baca=1⟩

Completion settings:

[1] aabc=1

Axiom: aabc=1.

Defines rule #3.

Referenced by [3].

[2] baca=1

Axiom: baca=1.

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

[3] bac=abc

Overlap of [2] baca=1 with [1] aabc=1:

bac a aabc

Critical pair: bac=abc.

Defines rule #1.

Referenced by [4], [5].

[4] abca=1

Overlap of [2] baca=1 with [3] bac=abc:

baca bac

Critical pair: abca=1.

Referenced by [5].

[5] bca=abc

Overlap of [2] baca=1 with [4] abca=1:

bac a abca

Critical pair: bac=bca.

Reduce LHS:

[3](bac)
⇒ abc

Flip LHS and RHS.

Defines rule #2.