Certificate for #7141 ⟨a, b | bb=aa, aaab=aa⟩

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], [5].

[2] aaab=aa

Axiom: aaab=aa.

Referenced by [4].

[3] aab=baa

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

b b bb

Critical pair: baa=aab.

Flip LHS and RHS.

Referenced by [4], [5], [6], [7], [8].

[4] abaa=aa

Simplify [2] aaab=aa.

Reduce LHS:

[3]	a(aab)
	⇒ abaa

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

[5] baa=aaaaa

Overlap of [4] abaa=aa with [3] aab=baa:

ab aa aab

Critical pair: abbaa=aab.

Reduce LHS:

[1]	a(bb)aa
	⇒ aaaaa

Reduce RHS:

[3]	(aab)
	⇒ baa

Flip LHS and RHS.

Defines rule #2.

Referenced by [6], [8].

[6] aaaaaaa=aaa

Overlap of [3] aab=baa with [4] abaa=aa:

a ab abaa

Critical pair: aaa=baaaa.

Reduce RHS:

[5]	(baa)aa
	⇒ aaaaaaa

Flip LHS and RHS.

Referenced by [7].

[7] aaaaaa=aa

Overlap of [6] aaaaaaa=aaa with [3] aab=baa:

aaaaa aa aab

Critical pair: aaaaabaa=aaab.

Reduce LHS:

[3]	aaa(aab)aa
[3]	⇒ a(aab)aaaa
[4]	⇒ (abaa)aaaa
	⇒ aaaaaa

Reduce RHS:

[3]	a(aab)
[4]	⇒ (abaa)
	⇒ aa

Defines rule #1.

[8] aab=aaaaa

Simplify [3] aab=baa.

Reduce RHS:

[5]	(baa)
	⇒ aaaaa

Defines rule #3.