Certificate for #3921 ⟨a, b | aaaababba=ba

Completion settings:

[1] aaaababba=ba

Axiom: aaaababba=ba.

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

[2] bbba=c

Axiom: bbba=c.

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

[3] bba=aaaabac

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

aaaababb a aaaababba

Critical pair: aaaababbba=baaaababba.

Reduce LHS:

[2]aaaaba(bbba)
aaaabac

Reduce RHS:

[1]b(aaaababba)
bba

Flip LHS and RHS.

Defines rule #1.

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

[4] caaabaaaaabac=bc

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

bbb a aaaababba

Critical pair: bbbba=caaababba.

Reduce LHS:

[2]b(bbba)
bc

Reduce RHS:

[3]caaaba(bba)
caaabaaaaabac

Flip LHS and RHS.

Defines rule #8.

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

[5] aaaababc=c

Overlap of [3] bba=aaaabac with [1] aaaababba=ba:

bb a aaaababba

Critical pair: bbba=aaaabacaaababba.

Reduce LHS:

[2](bbba)
c

Reduce RHS:

[3]aaaabacaaaba(bba)
[4]aaaaba(caaabaaaaabac)
aaaababc

Flip LHS and RHS.

Defines rule #4.

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

[6] bbbc=caaababc

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

bbb a aaaababc

Critical pair: bbbc=caaababc.

Referenced by [9].

[7] bbc=caaabac

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

caaabaaaaaba c caaabaaaaabac

Critical pair: caaabaaaaababc=bcaaabaaaaabac.

Reduce LHS:

[5]caaaba(aaaababc)
caaabac

Reduce RHS:

[4]b(caaabaaaaabac)
bbc

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[8] aaaabacaaabac=bc

Overlap of [5] aaaababc=c with [4] caaabaaaaabac=bc:

aaaabab c caaabaaaaabac

Critical pair: aaaababbc=caaabaaaaabac.

Reduce LHS:

[7]aaaaba(bbc)
aaaabacaaabac

Reduce RHS:

[4](caaabaaaaabac)
bc

Defines rule #6.

Referenced by [9].

[9] caaababc=bcaaabac

Overlap of [3] bba=aaaabac with [8] aaaabacaaabac=bc:

bb a aaaabacaaabac

Critical pair: bbbc=aaaabacaaabacaaabac.

Reduce LHS:

[6](bbbc)
caaababc

Reduce RHS:

[8](aaaabacaaabac)aaabac
bcaaabac

Defines rule #7.

[10] aaaabaaaaabac=ba

Overlap of [1] aaaababba=ba with [3] bba=aaaabac:

aaaaba bba bba

Critical pair: aaaabaaaaabac=ba.

Defines rule #5.

[11] baaaabac=c

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

b bba bba

Critical pair: baaaabac=c.

Defines rule #3.