Certificate for #4082 ⟨a, b | aabaaabba=ba

Completion settings:

[1] aabaaabba=ba

Axiom: aabaaabba=ba.

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

[2] bbba=c

Axiom: bbba=c.

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

[3] bba=aabaaac

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

aabaaabb a aabaaabba

Critical pair: aabaaabbba=baabaaabba.

Reduce LHS:

[2]aabaaa(bbba)
aabaaac

Reduce RHS:

[1]b(aabaaabba)
bba

Flip LHS and RHS.

Defines rule #1.

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

[4] cabaaaaabaaac=bc

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

bbb a aabaaabba

Critical pair: bbbba=cabaaabba.

Reduce LHS:

[2]b(bbba)
bc

Reduce RHS:

[3]cabaaa(bba)
cabaaaaabaaac

Flip LHS and RHS.

Defines rule #8.

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

[5] aabaaabc=c

Overlap of [3] bba=aabaaac with [1] aabaaabba=ba:

bb a aabaaabba

Critical pair: bbba=aabaaacabaaabba.

Reduce LHS:

[2](bbba)
c

Reduce RHS:

[3]aabaaacabaaa(bba)
[4]aabaaa(cabaaaaabaaac)
aabaaabc

Flip LHS and RHS.

Defines rule #4.

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

[6] bbbc=cabaaabc

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

bbb a aabaaabc

Critical pair: bbbc=cabaaabc.

Referenced by [9].

[7] bbc=cabaaac

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

cabaaaaabaaa c cabaaaaabaaac

Critical pair: cabaaaaabaaabc=bcabaaaaabaaac.

Reduce LHS:

[5]cabaaa(aabaaabc)
cabaaac

Reduce RHS:

[4]b(cabaaaaabaaac)
bbc

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[8] aabaaacabaaac=bc

Overlap of [5] aabaaabc=c with [4] cabaaaaabaaac=bc:

aabaaab c cabaaaaabaaac

Critical pair: aabaaabbc=cabaaaaabaaac.

Reduce LHS:

[7]aabaaa(bbc)
aabaaacabaaac

Reduce RHS:

[4](cabaaaaabaaac)
bc

Defines rule #6.

Referenced by [9].

[9] cabaaabc=bcabaaac

Overlap of [3] bba=aabaaac with [8] aabaaacabaaac=bc:

bb a aabaaacabaaac

Critical pair: bbbc=aabaaacabaaacabaaac.

Reduce LHS:

[6](bbbc)
cabaaabc

Reduce RHS:

[8](aabaaacabaaac)abaaac
bcabaaac

Defines rule #7.

[10] aabaaaaabaaac=ba

Overlap of [1] aabaaabba=ba with [3] bba=aabaaac:

aabaaa bba bba

Critical pair: aabaaaaabaaac=ba.

Defines rule #5.

[11] baabaaac=c

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

b bba bba

Critical pair: baabaaac=c.

Defines rule #3.