Certificate for #2453 ⟨a, b, c | aab=b, caac=1⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #6.

Referenced by [10].

[2] caac=1

Axiom: caac=1.

Referenced by [5], [6], [7], [8], [9].

[3] cc=d

Axiom: cc=d.

Defines rule #1.

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

[4] dc=cd

Overlap of [3] cc=d with [3] cc=d:

c c cc

Critical pair: cd=dc.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[5] aac=caa

Overlap of [2] caac=1 with [2] caac=1:

caa c caac

Critical pair: caa=aac.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7].

[6] caad=c

Overlap of [2] caac=1 with [3] cc=d:

caa c cc

Critical pair: caad=c.

Referenced by [8].

[7] cdaa=c

Overlap of [3] cc=d with [2] caac=1:

c c caac

Critical pair: c=daac.

Reduce RHS:

[5]d(aac)
[4]⇒ (dc)aa
⇒ cdaa

Flip LHS and RHS.

Referenced by [9].

[8] aad=1

Overlap of [2] caac=1 with [6] caad=c:

caa c caad

Critical pair: caac=aad.

Reduce LHS:

[2](caac)
⇒ 1

Flip LHS and RHS.

Defines rule #7.

Referenced by [11].

[9] daa=1

Overlap of [2] caac=1 with [7] cdaa=c:

caa c cdaa

Critical pair: caac=daa.

Reduce LHS:

[2](caac)
⇒ 1

Flip LHS and RHS.

Referenced by [10], [11].

[10] db=b

Overlap of [9] daa=1 with [1] aab=b:

d aa aab

Critical pair: db=b.

Defines rule #4.

[11] da=ad

Overlap of [9] daa=1 with [8] aad=1:

da a aad

Critical pair: da=ad.

Defines rule #3.