Certificate for #7050 ⟨a, b | bb=aa, ababa=a⟩

Completion settings:

Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1

[1] bb=aa

Axiom: bb=aa.

Defines rule #4.

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

[2] ababa=a

Axiom: ababa=a.

Defines rule #5.

Referenced by [4], [5], [8].

[3] aab=baa

Overlap of [1] bb=aa with [1] bb=aa:

b b bb

Critical pair: baa=aab.

Flip LHS and RHS.

Defines rule #3.

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

[4] abaaaaa=baa

Overlap of [2] ababa=a with [3] aab=baa:

abab a aab

Critical pair: ababbaa=aab.

Reduce LHS:

[1]	aba(bb)aa
	⇒ abaaaaa

Reduce RHS:

[3]	(aab)
	⇒ baa

Referenced by [7].

[5] babaaa=aa

Overlap of [3] aab=baa with [2] ababa=a:

a ab ababa

Critical pair: aa=baaaba.

Reduce RHS:

[3]	ba(aab)a
	⇒ babaaa

Flip LHS and RHS.

Referenced by [6].

[6] abaa=baaaaaaa

Overlap of [5] babaaa=aa with [3] aab=baa:

babaa a aab

Critical pair: babaabaa=aaab.

Reduce LHS:

[3]	bab(aab)aa
[1]	⇒ ba(bb)aaaa
	⇒ baaaaaaa

Reduce RHS:

[3]	a(aab)
	⇒ abaa

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[7] baaaaaaaaaa=baa

Simplify [4] abaaaaa=baa.

Reduce LHS:

[6]	(abaa)aaa
	⇒ baaaaaaaaaa

Referenced by [8].

[8] aaaaaaaaaa=aa

Overlap of [2] ababa=a with [7] baaaaaaaaaa=baa:

aba ba baaaaaaaaaa

Critical pair: ababaa=aaaaaaaaaa.

Reduce LHS:

[2]	(ababa)a
	⇒ aa

Flip LHS and RHS.

Defines rule #1.