Certificate for #6378 ⟨a, b | aab=a, bbbba=a⟩

Back:⟨a, b | aab=a, bbbba=a⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

Referenced by [3], [4], [5], [6], [7].

[2] bbbba=a

Axiom: bbbba=a.

Defines rule #3.

Referenced by [3].

[3] abbba=aaa

Overlap of [1] aab=a with [2] bbbba=a:

aa b bbbba

Critical pair: aaa=abbba.

Flip LHS and RHS.

Referenced by [4].

[4] aba=aaaaa

Overlap of [3] abbba=aaa with [3] abbba=aaa:

abbb a abbba

Critical pair: abbbaaa=aaabbba.

Reduce LHS:

[3](abbba)aa
⇒ aaaaa

Reduce RHS:

[1]a(aab)bba
[1]⇒ (aab)ba
⇒ aba

Flip LHS and RHS.

Referenced by [5], [6].

[5] aaaaaa=aa

Overlap of [1] aab=a with [4] aba=aaaaa:

a ab aba

Critical pair: aaaaaa=aa.

Referenced by [6].

[6] aaaaa=a

Overlap of [4] aba=aaaaa with [1] aab=a:

ab a aab

Critical pair: aba=aaaaaab.

Reduce LHS:

[4](aba)
⇒ aaaaa

Reduce RHS:

[5](aaaaaa)b
[1]⇒ (aab)
⇒ a

Defines rule #1.

Referenced by [7].

[7] ab=aaaa

Overlap of [6] aaaaa=a with [1] aab=a:

aaa aa aab

Critical pair: aaaa=ab.

Flip LHS and RHS.

Defines rule #2.