Certificate for #12537 ⟨a, b | abab=ba, baaa=b

Completion settings:

[1] abab=ba

Axiom: abab=ba.

Referenced by [3], [4], [8], [10], [12].

[2] baaa=b

Axiom: baaa=b.

Defines rule #1.

Referenced by [4], [5], [6], [8], [11], [12], [13], [14].

[3] abba=baab

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

ab ab abab

Critical pair: abba=baab.

Referenced by [5], [6], [7], [10].

[4] bbab=baaba

Overlap of [2] baaa=b with [1] abab=ba:

baa a abab

Critical pair: baaba=bbab.

Flip LHS and RHS.

Referenced by [7], [9].

[5] baabaab=bbba

Overlap of [2] baaa=b with [3] abba=baab:

baa a abba

Critical pair: baabaab=bbba.

Referenced by [8], [9].

[6] abb=baabaa

Overlap of [3] abba=baab with [2] baaa=b:

ab ba baaa

Critical pair: abb=baabaa.

Defines rule #4.

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

[7] babaabaa=abaaba

Overlap of [3] abba=baab with [4] bbab=baaba:

a bba bbab

Critical pair: abaaba=baabb.

Reduce RHS:

[6]ba(abb)
babaabaa

Flip LHS and RHS.

Referenced by [8].

[8] bbbb=b

Overlap of [5] baabaab=bbba with [5] baabaab=bbba:

baa baab baabaab

Critical pair: baabbba=bbbaaab.

Reduce LHS:

[6]ba(abb)ba
[7](babaabaa)ba
[1]aba(abab)a
[1](abab)aa
[2](baaa)
b

Reduce RHS:

[2]bb(baaa)b
bbbb

Flip LHS and RHS.

Defines rule #7.

Referenced by [9].

[9] bbaaba=ab

Overlap of [6] abb=baabaa with [8] bbbb=b:

a bb bbbb

Critical pair: ab=baabaabb.

Reduce RHS:

[5](baabaab)b
[4]b(bbab)
bbaaba

Flip LHS and RHS.

Referenced by [10], [11].

[10] babaa=aab

Overlap of [3] abba=baab with [9] bbaaba=ab:

a bba bbaaba

Critical pair: aab=baababa.

Reduce RHS:

[1]ba(abab)a
babaa

Flip LHS and RHS.

Referenced by [12], [13].

[11] bbaab=abaa

Overlap of [9] bbaaba=ab with [2] baaa=b:

bbaa ba baaa

Critical pair: bbaab=abaa.

Defines rule #6.

[12] aaab=b

Overlap of [1] abab=ba with [10] babaa=aab:

a bab babaa

Critical pair: aaab=baaa.

Reduce RHS:

[2](baaa)
b

Defines rule #2.

[13] bab=aaba

Overlap of [10] babaa=aab with [2] baaa=b:

ba baa baaa

Critical pair: bab=aaba.

Defines rule #3.

Referenced by [14].

[14] aabaab=bba

Overlap of [13] bab=aaba with [13] bab=aaba:

ba b bab

Critical pair: baaaba=aabaab.

Reduce LHS:

[2](baaa)ba
bba

Flip LHS and RHS.

Defines rule #5.