Certificate for #5285 ⟨a, b | aba=bb, abba=b⟩

Completion settings:

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

[1] aba=bb

Axiom: aba=bb.

Referenced by [3], [4], [5], [6], [8].

[2] abba=b

Axiom: abba=b.

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

[3] bbba=abbb

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

ab a aba

Critical pair: abbb=bbba.

Flip LHS and RHS.

Referenced by [4], [9].

[4] babbb=abb

Overlap of [1] aba=bb with [2] abba=b:

ab a abba

Critical pair: abb=bbbba.

Reduce RHS:

[3]	b(bbba)
	⇒ babbb

Flip LHS and RHS.

Referenced by [6], [7].

[5] bba=abbbb

Overlap of [2] abba=b with [1] aba=bb:

abb a aba

Critical pair: abbbb=bba.

Flip LHS and RHS.

Referenced by [6], [7], [9].

[6] bbbbbbb=b

Overlap of [4] babbb=abb with [5] bba=abbbb:

bab bb bba

Critical pair: bababbbb=abba.

Reduce LHS:

[1]	b(aba)bbbb
	⇒ bbbbbbb

Reduce RHS:

[2]	(abba)
	⇒ b

Defines rule #1.

Referenced by [7], [9].

[7] babb=ab

Overlap of [5] bba=abbbb with [4] babbb=abb:

b ba babbb

Critical pair: babb=abbbbbbb.

Reduce RHS:

[6]	a(bbbbbbb)
	⇒ ab

Referenced by [8].

[8] aab=bbbb

Overlap of [1] aba=bb with [7] babb=ab:

a ba babb

Critical pair: aab=bbbb.

Defines rule #3.

[9] ba=abbbbb

Overlap of [6] bbbbbbb=b with [5] bba=abbbb:

bbbbb bb bba

Critical pair: bbbbbabbbb=ba.

Reduce LHS:

[3]	bb(bbba)bbbb
[6]	⇒ bba(bbbbbbb)
[5]	⇒ (bba)b
	⇒ abbbbb

Flip LHS and RHS.

Defines rule #2.