Certificate for #19264 ⟨a, b | aaa=a, abaab=ba

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #5.

Referenced by [3], [4], [7].

[2] abaab=ba

Axiom: abaab=ba.

Referenced by [3], [4], [5], [6], [9].

[3] aaba=ba

Overlap of [1] aaa=a with [2] abaab=ba:

aa a abaab

Critical pair: aaba=abaab.

Reduce RHS:

[2](abaab)
ba

Defines rule #6.

Referenced by [5], [6], [8], [10].

[4] ababa=bab

Overlap of [2] abaab=ba with [2] abaab=ba:

aba ab abaab

Critical pair: ababa=baaab.

Reduce RHS:

[1]b(aaa)b
bab

Referenced by [8].

[5] baa=abba

Overlap of [2] abaab=ba with [3] aaba=ba:

ab aab aaba

Critical pair: abba=baa.

Flip LHS and RHS.

Referenced by [6], [7], [8], [9], [11].

[6] abbab=aba

Overlap of [3] aaba=ba with [2] abaab=ba:

a aba abaab

Critical pair: aba=baab.

Reduce RHS:

[5](baa)b
abbab

Flip LHS and RHS.

Referenced by [8], [9].

[7] ababba=ba

Overlap of [5] baa=abba with [1] aaa=a:

b aa aaa

Critical pair: ba=abbaa.

Reduce RHS:

[5]ab(baa)
ababba

Flip LHS and RHS.

Referenced by [10].

[8] bba=babb

Overlap of [5] baa=abba with [6] abbab=aba:

ba a abbab

Critical pair: baaba=abbabbab.

Reduce LHS:

[3]b(aaba)
bba

Reduce RHS:

[6](abbab)bab
[4](ababa)b
babb

Defines rule #2.

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

[9] baba=abab

Overlap of [2] abaab=ba with [8] bba=babb:

abaa b bba

Critical pair: abaababb=baba.

Reduce LHS:

[2](abaab)abb
[5](baa)bb
[6](abbab)b
abab

Flip LHS and RHS.

Defines rule #4.

Referenced by [10].

[10] babbb=ba

Overlap of [9] baba=abab with [9] baba=abab:

ba ba baba

Critical pair: baabab=ababba.

Reduce LHS:

[3]b(aaba)b
[8](bba)b
babbb

Reduce RHS:

[7](ababba)
ba

Defines rule #1.

[11] baa=ababb

Simplify [5] baa=abba.

Reduce RHS:

[8]a(bba)
ababb

Defines rule #3.