Certificate for #4585 ⟨a, b | aaabbbba=baa

Completion settings:

[1] aaabbbba=baa

Axiom: aaabbbba=baa.

Referenced by [4].

[2] bbbb=c

Axiom: bbbb=c.

Defines rule #10.

Referenced by [4], [5], [6], [8].

[3] caa=d

Axiom: caa=d.

Defines rule #4.

Referenced by [6], [7], [8], [9], [10], [11].

[4] baa=aaaca

Overlap of [1] aaabbbba=baa with [2] bbbb=c:

aaa bbbba bbbb

Critical pair: aaaca=baa.

Flip LHS and RHS.

Defines rule #7.

Referenced by [6], [7], [10].

[5] cb=bc

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

b bbb bbbb

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [7].

[6] aaadddca=d

Overlap of [2] bbbb=c with [4] baa=aaaca:

bbb b baa

Critical pair: bbbaaaca=caa.

Reduce LHS:

[4]bb(baa)aca
[4]b(baa)acaaca
[4](baa)acaacaaca
[3]aaa(caa)caacaaca
[3]aaad(caa)caaca
[3]aaadd(caa)ca
aaadddca

Reduce RHS:

[3](caa)
d

Defines rule #2.

Referenced by [9], [10], [11].

[7] bd=daca

Overlap of [5] cb=bc with [4] baa=aaaca:

c b baa

Critical pair: caaaca=bcaa.

Reduce LHS:

[3](caa)aca
daca

Reduce RHS:

[3]b(caa)
bd

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

[8] cd=dadddca

Overlap of [2] bbbb=c with [7] bd=daca:

bbb b bd

Critical pair: bbbdaca=cd.

Reduce LHS:

[7]bb(bd)aca
[7]b(bd)acaaca
[7](bd)acaacaaca
[3]da(caa)caacaaca
[3]dad(caa)caaca
[3]dadd(caa)ca
dadddca

Flip LHS and RHS.

Defines rule #3.

[9] cad=daadddca

Overlap of [3] caa=d with [6] aaadddca=d:

ca a aaadddca

Critical pair: cad=daadddca.

Defines rule #5.

[10] bad=aaadadddca

Overlap of [4] baa=aaaca with [6] aaadddca=d:

ba a aaadddca

Critical pair: bad=aaacaaadddca.

Reduce RHS:

[3]aaa(caa)adddca
aaadadddca

Defines rule #8.

[11] aaadddd=da

Overlap of [6] aaadddca=d with [3] caa=d:

aaaddd ca caa

Critical pair: aaadddd=da.

Defines rule #1.