Certificate for #2203 ⟨a, b | aaabbba=baa

Completion settings:

[1] aaabbba=baa

Axiom: aaabbba=baa.

Referenced by [4].

[2] bbb=c

Axiom: bbb=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] aaabbba=baa with [2] bbb=c:

aaa bbba bbb

Critical pair: aaaca=baa.

Flip LHS and RHS.

Defines rule #7.

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

[5] cb=bc

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

b bb bbb

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [7].

[6] aaaddca=d

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

bb b baa

Critical pair: bbaaaca=caa.

Reduce LHS:

[4]b(baa)aca
[4](baa)acaaca
[3]aaa(caa)caaca
[3]aaad(caa)ca
aaaddca

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=daddca

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

bb b bd

Critical pair: bbdaca=cd.

Reduce LHS:

[7]b(bd)aca
[7](bd)acaaca
[3]da(caa)caaca
[3]dad(caa)ca
daddca

Flip LHS and RHS.

Defines rule #3.

[9] cad=daaddca

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

ca a aaaddca

Critical pair: cad=daaddca.

Defines rule #5.

[10] bad=aaadaddca

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

ba a aaaddca

Critical pair: bad=aaacaaaddca.

Reduce RHS:

[3]aaa(caa)addca
aaadaddca

Defines rule #8.

[11] aaaddd=da

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

aaadd ca caa

Critical pair: aaaddd=da.

Defines rule #1.