Certificate for #11058 ⟨a, b | abba=bbb, baba=1⟩

Completion settings:

[1] abba=bbb

Axiom: abba=bbb.

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

[2] baba=1

Axiom: baba=1.

Referenced by [4], [5], [7], [8], [9], [11].

[3] bbbbba=abbbbb

Overlap of [1] abba=bbb with [1] abba=bbb:

abb a abba

Critical pair: abbbbb=bbbbba.

Flip LHS and RHS.

Referenced by [9], [11].

[4] bbbba=ab

Overlap of [1] abba=bbb with [2] baba=1:

ab ba baba

Critical pair: ab=bbbba.

Flip LHS and RHS.

Referenced by [6].

[5] bba=babbbb

Overlap of [2] baba=1 with [1] abba=bbb:

bab a abba

Critical pair: babbbb=bba.

Flip LHS and RHS.

Referenced by [6], [9], [10], [12].

[6] babbbbbbbbbbbb=ab

Simplify [4] bbbba=ab.

Reduce LHS:

[5]bb(bba)
[5]b(bba)bbbb
[5](bba)bbbbbbbb
babbbbbbbbbbbb

Referenced by [7], [8], [10].

[7] baab=bbbbbbbbbbbb

Overlap of [2] baba=1 with [6] babbbbbbbbbbbb=ab:

ba ba babbbbbbbbbbbb

Critical pair: baab=bbbbbbbbbbbb.

Referenced by [9].

[8] babbbbbbbbbbb=a

Overlap of [6] babbbbbbbbbbbb=ab with [2] baba=1:

babbbbbbbbbbb b baba

Critical pair: babbbbbbbbbbb=ababa.

Reduce RHS:

[2]a(baba)
a

Referenced by [10].

[9] bbbbbbbbbbbbbbbb=b

Overlap of [5] bba=babbbb with [2] baba=1:

b ba baba

Critical pair: b=babbbbba.

Reduce RHS:

[3]ba(bbbbba)
[7](baab)bbbb
bbbbbbbbbbbbbbbb

Flip LHS and RHS.

Referenced by [13].

[10] bab=abbbbb

Overlap of [5] bba=babbbb with [6] babbbbbbbbbbbb=ab:

b ba babbbbbbbbbbbb

Critical pair: bab=babbbbbbbbbbbbbbbb.

Reduce RHS:

[8](babbbbbbbbbbb)bbbbb
abbbbb

Referenced by [11].

[11] aabbbbb=1

Overlap of [2] baba=1 with [10] bab=abbbbb:

baba bab

Critical pair: abbbbba=1.

Reduce LHS:

[3]a(bbbbba)
aabbbbb

Referenced by [12], [13], [14], [15].

[12] ba=abbbb

Overlap of [11] aabbbbb=1 with [5] bba=babbbb:

aabbbb b bba

Critical pair: aabbbbbabbbb=ba.

Reduce LHS:

[11](aabbbbb)abbbb
abbbb

Flip LHS and RHS.

Defines rule #2.

[13] aab=bbbbbbbbbbb

Overlap of [11] aabbbbb=1 with [9] bbbbbbbbbbbbbbbb=b:

aa bbbbb bbbbbbbbbbbbbbbb

Critical pair: aab=bbbbbbbbbbb.

Referenced by [14].

[14] bbbbbbbbbbbbbbb=1

Overlap of [11] aabbbbb=1 with [13] aab=bbbbbbbbbbb:

aabbbbb aab

Critical pair: bbbbbbbbbbbbbbb=1.

Defines rule #1.

Referenced by [15].

[15] aa=bbbbbbbbbb

Overlap of [11] aabbbbb=1 with [14] bbbbbbbbbbbbbbb=1:

aa bbbbb bbbbbbbbbbbbbbb

Critical pair: aa=bbbbbbbbbb.

Defines rule #3.