Certificate for #7154 ⟨a, b | bb=aa, abab=ba⟩

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] abab=ba

Axiom: abab=ba.

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

[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 [5], [6], [7].

[4] bab=abaaa

Overlap of [2] abab=ba with [1] bb=aa:

aba b bb

Critical pair: abaaa=bab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [6].

[5] abaaaaa=aba

Overlap of [3] aab=baa with [2] abab=ba:

a ab abab

Critical pair: aba=baaab.

Reduce RHS:

[3]	ba(aab)
[4]	⇒ (bab)aa
	⇒ abaaaaa

Flip LHS and RHS.

Referenced by [7].

[6] aaaaaaa=aaa

Overlap of [4] bab=abaaa with [2] abab=ba:

b ab abab

Critical pair: bba=abaaaab.

Reduce LHS:

[1]	(bb)a
	⇒ aaa

Reduce RHS:

[3]	abaa(aab)
[3]	⇒ ab(aab)aa
[1]	⇒ a(bb)aaaa
	⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #1.

[7] baaaaa=ba

Overlap of [5] abaaaaa=aba with [3] aab=baa:

abaaa aa aab

Critical pair: abaaabaa=abab.

Reduce LHS:

[3]	aba(aab)aa
[2]	⇒ (abab)aaaa
	⇒ baaaaa

Reduce RHS:

[2]	(abab)
	⇒ ba

Defines rule #2.