Certificate for #5383 ⟨a, b | aab=ab, bab=aa⟩

Back:⟨a, b | aab=ab, bab=aa⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

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

[2] bab=aa

Axiom: bab=aa.

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

[3] aaaa=aaa

Overlap of [1] aab=ab with [2] bab=aa:

aa b bab

Critical pair: aaaa=abab.

Reduce RHS:

[2]a(bab)
⇒ aaa

Referenced by [5].

[4] ab=baaa

Overlap of [2] bab=aa with [2] bab=aa:

ba b bab

Critical pair: baaa=aaab.

Reduce RHS:

[1]a(aab)
[1]⇒ (aab)
⇒ ab

Flip LHS and RHS.

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

[5] aaa=aa

Overlap of [4] ab=baaa with [2] bab=aa:

a b bab

Critical pair: aaa=baaaab.

Reduce RHS:

[3]b(aaaa)b
[1]⇒ ba(aab)
[1]⇒ b(aab)
[2]⇒ (bab)
⇒ aa

Defines rule #1.

Referenced by [6], [7].

[6] bbaa=aa

Overlap of [2] bab=aa with [4] ab=baaa:

b ab ab

Critical pair: bbaaa=aa.

Reduce LHS:

[5]bb(aaa)
⇒ bbaa

Defines rule #3.

[7] ab=baa

Simplify [4] ab=baaa.

Reduce RHS:

[5]b(aaa)
⇒ baa

Defines rule #2.