Certificate for #5349 ⟨a, b | aaa=bb, bab=aa⟩

Completion settings:

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

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #5.

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

[2] bab=aa

Axiom: bab=aa.

Defines rule #6.

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

[3] aaab=baaa

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

b b bb

Critical pair: baaa=aaab.

Flip LHS and RHS.

Referenced by [4].

[4] abaaa=baa

Overlap of [1] bb=aaa with [2] bab=aa:

b b bab

Critical pair: baa=aaaab.

Reduce RHS:

[3]	a(aaab)
	⇒ abaaa

Flip LHS and RHS.

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

[5] aab=baaaa

Overlap of [2] bab=aa with [1] bb=aaa:

ba b bb

Critical pair: baaaa=aab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [7].

[6] aaaaaaaaaa=aaaa

Overlap of [4] abaaa=baa with [4] abaaa=baa:

abaa a abaaa

Critical pair: abaabaa=baabaaa.

Reduce LHS:

[5]	ab(aab)aa
[1]	⇒ a(bb)aaaaaa
	⇒ aaaaaaaaaa

Reduce RHS:

[4]	ba(abaaa)
[2]	⇒ (bab)aa
	⇒ aaaa

Defines rule #1.

[7] abaa=baaaaaaa

Overlap of [5] aab=baaaa with [4] abaaa=baa:

a ab abaaa

Critical pair: abaa=baaaaaaa.

Defines rule #3.

Referenced by [8].

[8] baaaaaaaa=baa

Overlap of [4] abaaa=baa with [7] abaa=baaaaaaa:

abaaa abaa

Critical pair: baaaaaaaa=baa.

Defines rule #2.