Certificate for #19021 ⟨a, b | aab=b, abbbba=b⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3], [4], [5], [8], [9], [10].

[2] abbbba=b

Axiom: abbbba=b.

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

[3] bbbba=ab

Overlap of [1] aab=b with [2] abbbba=b:

a ab abbbba

Critical pair: ab=bbbba.

Flip LHS and RHS.

Referenced by [6], [7].

[4] bab=abbbbb

Overlap of [2] abbbba=b with [1] aab=b:

abbbb a aab

Critical pair: abbbbb=bab.

Flip LHS and RHS.

Referenced by [5], [6], [7], [9].

[5] bbbbbbbbbbbbbbbbb=bb

Overlap of [2] abbbba=b with [4] bab=abbbbb:

abbb ba bab

Critical pair: abbbabbbbb=bb.

Reduce LHS:

[4]abb(bab)bbbb
[4]⇒ ab(bab)bbbbbbbb
[4]⇒ a(bab)bbbbbbbbbbbb
[1]⇒ (aab)bbbbbbbbbbbbbbbb
⇒ bbbbbbbbbbbbbbbbb

Referenced by [6].

[6] bba=abbbbbbbb

Overlap of [5] bbbbbbbbbbbbbbbbb=bb with [3] bbbba=ab:

bbbbbbbbbbbbb bbbb bbbba

Critical pair: bbbbbbbbbbbbbab=bba.

Reduce LHS:

[3]bbbbbbbbb(bbbba)b
[3]⇒ bbbbb(bbbba)bb
[3]⇒ b(bbbba)bbb
[4]⇒ (bab)bbb
⇒ abbbbbbbb

Flip LHS and RHS.

Referenced by [7], [9].

[7] abbbbbbbbbbbbbbbb=ab

Overlap of [3] bbbba=ab with [6] bba=abbbbbbbb:

bb bba bba

Critical pair: bbabbbbbbbb=ab.

Reduce LHS:

[4]b(bab)bbbbbbb
[4]⇒ (bab)bbbbbbbbbbb
⇒ abbbbbbbbbbbbbbbb

Referenced by [8], [9].

[8] bbbbbbbbbbbbbbbb=b

Overlap of [1] aab=b with [7] abbbbbbbbbbbbbbbb=ab:

a ab abbbbbbbbbbbbbbbb

Critical pair: aab=bbbbbbbbbbbbbbbb.

Reduce LHS:

[1](aab)
⇒ b

Flip LHS and RHS.

Defines rule #1.

Referenced by [9].

[9] aba=bbbb

Overlap of [7] abbbbbbbbbbbbbbbb=ab with [6] bba=abbbbbbbb:

abbbbbbbbbbbbbb bb bba

Critical pair: abbbbbbbbbbbbbbabbbbbbbb=aba.

Reduce LHS:

[4]abbbbbbbbbbbbb(bab)bbbbbbb
[4]⇒ abbbbbbbbbbbb(bab)bbbbbbbbbbb
[7]⇒ abbbbbbbbbbbb(abbbbbbbbbbbbbbbb)
[4]⇒ abbbbbbbbbbb(bab)
[4]⇒ abbbbbbbbbb(bab)bbbb
[4]⇒ abbbbbbbbb(bab)bbbbbbbb
[4]⇒ abbbbbbbb(bab)bbbbbbbbbbbb
[7]⇒ abbbbbbbb(abbbbbbbbbbbbbbbb)b
[4]⇒ abbbbbbb(bab)b
[4]⇒ abbbbbb(bab)bbbbb
[4]⇒ abbbbb(bab)bbbbbbbbb
[4]⇒ abbbb(bab)bbbbbbbbbbbbb
[7]⇒ abbbb(abbbbbbbbbbbbbbbb)bb
[4]⇒ abbb(bab)bb
[4]⇒ abb(bab)bbbbbb
[4]⇒ ab(bab)bbbbbbbbbb
[4]⇒ a(bab)bbbbbbbbbbbbbb
[1]⇒ (aab)bbbbbbbbbbbbbbbbbb
[8]⇒ (bbbbbbbbbbbbbbbb)bbb
⇒ bbbb

Flip LHS and RHS.

Referenced by [10].

[10] ba=abbbb

Overlap of [1] aab=b with [9] aba=bbbb:

a ab aba

Critical pair: abbbb=ba.

Flip LHS and RHS.

Defines rule #2.