Certificate for #16506 ⟨a, b | aab=ab, bbb=aaa⟩

Back:⟨a, b | aab=ab, bbb=aaa⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

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

[2] bbb=aaa

Axiom: bbb=aaa.

Defines rule #4.

Referenced by [3], [4].

[3] aaaaa=aaaa

Overlap of [1] aab=ab with [2] bbb=aaa:

aa b bbb

Critical pair: aaaaa=abbb.

Reduce RHS:

[2]a(bbb)
⇒ aaaa

Defines rule #1.

Referenced by [5].

[4] ab=baaa

Overlap of [2] bbb=aaa with [2] bbb=aaa:

b bb bbb

Critical pair: baaa=aaab.

Reduce RHS:

[1]a(aab)
[1]⇒ (aab)
⇒ ab

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] baaaa=baaa

Overlap of [3] aaaaa=aaaa with [4] ab=baaa:

aaaa a ab

Critical pair: aaaabaaa=aaaab.

Reduce LHS:

[1]aa(aab)aaa
[1]⇒ a(aab)aaa
[1]⇒ (aab)aaa
[4]⇒ (ab)aaa
[3]⇒ b(aaaaa)a
[3]⇒ b(aaaaa)
⇒ baaaa

Reduce RHS:

[1]aa(aab)
[1]⇒ a(aab)
[1]⇒ (aab)
[4]⇒ (ab)
⇒ baaa

Defines rule #2.