Certificate for #6402 ⟨a, b | aab=b, ababa=a⟩

Back:⟨a, b | aab=b, ababa=a⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #2.

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

[2] ababa=a

Axiom: ababa=a.

Referenced by [3], [6].

[3] baba=aa

Overlap of [1] aab=b with [2] ababa=a:

a ab ababa

Critical pair: aa=baba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

[4] babb=ab

Overlap of [3] baba=aa with [1] aab=b:

bab a aab

Critical pair: babb=aaab.

Reduce RHS:

[1]a(aab)
⇒ ab

Defines rule #4.

[5] baaa=ba

Overlap of [3] baba=aa with [3] baba=aa:

ba ba baba

Critical pair: baaa=aaba.

Reduce RHS:

[1](aab)a
⇒ ba

Referenced by [6].

[6] aaa=a

Overlap of [2] ababa=a with [5] baaa=ba:

aba ba baaa

Critical pair: ababa=aaa.

Reduce LHS:

[2](ababa)
⇒ a

Flip LHS and RHS.

Defines rule #1.