Certificate for #5551 ⟨a, b | aaabaa=baaba

Completion settings:

[1] aaabaa=baaba

Axiom: aaabaa=baaba.

Referenced by [3].

[2] aaba=c

Axiom: aaba=c.

Defines rule #2.

Referenced by [3], [4], [6], [7], [8], [10].

[3] aaabaa=bc

Simplify [1] aaabaa=baaba.

Reduce RHS:

[2]b(aaba)
bc

Referenced by [4].

[4] aca=bc

Overlap of [3] aaabaa=bc with [2] aaba=c:

a aabaa aaba

Critical pair: aca=bc.

Defines rule #1.

Referenced by [5], [7], [8], [9], [11].

[5] acbc=bcca

Overlap of [4] aca=bc with [4] aca=bc:

ac a aca

Critical pair: acbc=bcca.

Defines rule #4.

[6] aabc=caba

Overlap of [2] aaba=c with [2] aaba=c:

aab a aaba

Critical pair: aabc=caba.

Defines rule #3.

Referenced by [9], [10], [12].

[7] aabbc=cca

Overlap of [2] aaba=c with [4] aca=bc:

aab a aca

Critical pair: aabbc=cca.

Defines rule #6.

Referenced by [13].

[8] bcaba=acc

Overlap of [4] aca=bc with [2] aaba=c:

ac a aaba

Critical pair: acc=bcaba.

Flip LHS and RHS.

Defines rule #5.

Referenced by [10], [11], [12], [13], [14].

[9] accaba=bcabc

Overlap of [4] aca=bc with [6] aabc=caba:

ac a aabc

Critical pair: accaba=bcabc.

Defines rule #8.

[10] aaacc=cabc

Overlap of [6] aabc=caba with [8] bcaba=acc:

aa bc bcaba

Critical pair: aaacc=cabaaba.

Reduce RHS:

[2]cab(aaba)
cabc

Defines rule #7.

Referenced by [14].

[11] bcabbc=accca

Overlap of [8] bcaba=acc with [4] aca=bc:

bcab a aca

Critical pair: bcabbc=accca.

Defines rule #9.

[12] bcaacc=accabc

Overlap of [8] bcaba=acc with [6] aabc=caba:

bcab a aabc

Critical pair: bcabcaba=accabc.

Reduce LHS:

[8]bca(bcaba)
bcaacc

Defines rule #10.

[13] accabbc=bcabcca

Overlap of [8] bcaba=acc with [7] aabbc=cca:

bcab a aabbc

Critical pair: bcabcca=accabbc.

Flip LHS and RHS.

Defines rule #11.

[14] bcabcabc=accaacc

Overlap of [8] bcaba=acc with [10] aaacc=cabc:

bcab a aaacc

Critical pair: bcabcabc=accaacc.

Defines rule #12.