Certificate for #3977 ⟨a, b | aaabaabba=ba

Completion settings:

[1] aaabaabba=ba

Axiom: aaabaabba=ba.

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

[2] bbba=c

Axiom: bbba=c.

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

[3] bba=aaabaac

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

aaabaabb a aaabaabba

Critical pair: aaabaabbba=baaabaabba.

Reduce LHS:

[2]aaabaa(bbba)
aaabaac

Reduce RHS:

[1]b(aaabaabba)
bba

Flip LHS and RHS.

Defines rule #1.

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

[4] caabaaaaabaac=bc

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

bbb a aaabaabba

Critical pair: bbbba=caabaabba.

Reduce LHS:

[2]b(bbba)
bc

Reduce RHS:

[3]caabaa(bba)
caabaaaaabaac

Flip LHS and RHS.

Defines rule #8.

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

[5] aaabaabc=c

Overlap of [3] bba=aaabaac with [1] aaabaabba=ba:

bb a aaabaabba

Critical pair: bbba=aaabaacaabaabba.

Reduce LHS:

[2](bbba)
c

Reduce RHS:

[3]aaabaacaabaa(bba)
[4]aaabaa(caabaaaaabaac)
aaabaabc

Flip LHS and RHS.

Defines rule #4.

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

[6] bbbc=caabaabc

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

bbb a aaabaabc

Critical pair: bbbc=caabaabc.

Referenced by [9].

[7] bbc=caabaac

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

caabaaaaabaa c caabaaaaabaac

Critical pair: caabaaaaabaabc=bcaabaaaaabaac.

Reduce LHS:

[5]caabaa(aaabaabc)
caabaac

Reduce RHS:

[4]b(caabaaaaabaac)
bbc

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[8] aaabaacaabaac=bc

Overlap of [5] aaabaabc=c with [4] caabaaaaabaac=bc:

aaabaab c caabaaaaabaac

Critical pair: aaabaabbc=caabaaaaabaac.

Reduce LHS:

[7]aaabaa(bbc)
aaabaacaabaac

Reduce RHS:

[4](caabaaaaabaac)
bc

Defines rule #6.

Referenced by [9].

[9] caabaabc=bcaabaac

Overlap of [3] bba=aaabaac with [8] aaabaacaabaac=bc:

bb a aaabaacaabaac

Critical pair: bbbc=aaabaacaabaacaabaac.

Reduce LHS:

[6](bbbc)
caabaabc

Reduce RHS:

[8](aaabaacaabaac)aabaac
bcaabaac

Defines rule #7.

[10] aaabaaaaabaac=ba

Overlap of [1] aaabaabba=ba with [3] bba=aaabaac:

aaabaa bba bba

Critical pair: aaabaaaaabaac=ba.

Defines rule #5.

[11] baaabaac=c

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

b bba bba

Critical pair: baaabaac=c.

Defines rule #3.