Certificate for #4238 ⟨a, b | abaaaabba=ba

Completion settings:

[1] abaaaabba=ba

Axiom: abaaaabba=ba.

Referenced by [3], [4], [5], [10].

[2] bbba=c

Axiom: bbba=c.

Referenced by [3], [4], [5], [6], [11].

[3] bba=abaaaac

Overlap of [1] abaaaabba=ba with [1] abaaaabba=ba:

abaaaabb a abaaaabba

Critical pair: abaaaabbba=babaaaabba.

Reduce LHS:

[2]abaaaa(bbba)
abaaaac

Reduce RHS:

[1]b(abaaaabba)
bba

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [5], [9], [10], [11].

[4] cbaaaaabaaaac=bc

Overlap of [2] bbba=c with [1] abaaaabba=ba:

bbb a abaaaabba

Critical pair: bbbba=cbaaaabba.

Reduce LHS:

[2]b(bbba)
bc

Reduce RHS:

[3]cbaaaa(bba)
cbaaaaabaaaac

Flip LHS and RHS.

Defines rule #8.

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

[5] abaaaabc=c

Overlap of [3] bba=abaaaac with [1] abaaaabba=ba:

bb a abaaaabba

Critical pair: bbba=abaaaacbaaaabba.

Reduce LHS:

[2](bbba)
c

Reduce RHS:

[3]abaaaacbaaaa(bba)
[4]abaaaa(cbaaaaabaaaac)
abaaaabc

Flip LHS and RHS.

Defines rule #4.

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

[6] bbbc=cbaaaabc

Overlap of [2] bbba=c with [5] abaaaabc=c:

bbb a abaaaabc

Critical pair: bbbc=cbaaaabc.

Referenced by [9].

[7] bbc=cbaaaac

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

cbaaaaabaaaa c cbaaaaabaaaac

Critical pair: cbaaaaabaaaabc=bcbaaaaabaaaac.

Reduce LHS:

[5]cbaaaa(abaaaabc)
cbaaaac

Reduce RHS:

[4]b(cbaaaaabaaaac)
bbc

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[8] abaaaacbaaaac=bc

Overlap of [5] abaaaabc=c with [4] cbaaaaabaaaac=bc:

abaaaab c cbaaaaabaaaac

Critical pair: abaaaabbc=cbaaaaabaaaac.

Reduce LHS:

[7]abaaaa(bbc)
abaaaacbaaaac

Reduce RHS:

[4](cbaaaaabaaaac)
bc

Defines rule #6.

Referenced by [9].

[9] cbaaaabc=bcbaaaac

Overlap of [3] bba=abaaaac with [8] abaaaacbaaaac=bc:

bb a abaaaacbaaaac

Critical pair: bbbc=abaaaacbaaaacbaaaac.

Reduce LHS:

[6](bbbc)
cbaaaabc

Reduce RHS:

[8](abaaaacbaaaac)baaaac
bcbaaaac

Defines rule #7.

[10] abaaaaabaaaac=ba

Overlap of [1] abaaaabba=ba with [3] bba=abaaaac:

abaaaa bba bba

Critical pair: abaaaaabaaaac=ba.

Defines rule #5.

[11] babaaaac=c

Overlap of [2] bbba=c with [3] bba=abaaaac:

b bba bba

Critical pair: babaaaac=c.

Defines rule #3.