Certificate for #18750 ⟨a, b | aaa=a, babbab=a⟩

Back:⟨a, b | aaa=a, babbab=a⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #2.

Referenced by [5], [7].

[2] babbab=a

Axiom: babbab=a.

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

[3] baba=abab

Overlap of [2] babbab=a with [2] babbab=a:

bab bab babbab

Critical pair: baba=abab.

Referenced by [4], [5].

[4] ababbbab=baa

Overlap of [3] baba=abab with [2] babbab=a:

ba ba babbab

Critical pair: baa=ababbbab.

Flip LHS and RHS.

Referenced by [5].

[5] ba=ab

Overlap of [4] ababbbab=baa with [3] baba=abab:

ababb bab baba

Critical pair: ababbabab=baaa.

Reduce LHS:

[2]a(babbab)ab
[1]⇒ (aaa)b
⇒ ab

Reduce RHS:

[1]b(aaa)
⇒ ba

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

[6] aabbbb=a

Overlap of [2] babbab=a with [5] ba=ab:

babbab ba

Critical pair: abbbab=a.

Reduce LHS:

[5]abb(ba)b
[5]⇒ ab(ba)bb
[5]⇒ a(ba)bbb
⇒ aabbbb

Referenced by [7].

[7] abbbb=aa

Overlap of [1] aaa=a with [6] aabbbb=a:

a aa aabbbb

Critical pair: aa=abbbb.

Flip LHS and RHS.

Defines rule #3.