Certificate for #7153 ⟨a, b | bb=aa, abab=ab⟩

Completion settings:

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

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #5.

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

[2] abab=ab

Axiom: abab=ab.

Defines rule #6.

Referenced by [4], [5].

[3] bba=abb

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

a a aa

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #4.

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

[4] babbb=bbb

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

a a abab

Critical pair: aab=bbbab.

Reduce LHS:

[1]	(aa)b
	⇒ bbb

Reduce RHS:

[3]	b(bba)b
	⇒ babbb

Flip LHS and RHS.

Defines rule #3.

Referenced by [6].

[5] abbbbb=bbbb

Overlap of [2] abab=ab with [3] bba=abb:

aba b bba

Critical pair: abaabb=abba.

Reduce LHS:

[1]	ab(aa)bb
	⇒ abbbbb

Reduce RHS:

[3]	a(bba)
[1]	⇒ (aa)bb
	⇒ bbbb

Referenced by [7].

[6] abbbb=bbbbbbb

Overlap of [4] babbb=bbb with [3] bba=abb:

babb b bba

Critical pair: babbabb=bbbba.

Reduce LHS:

[3]	ba(bba)bb
[1]	⇒ b(aa)bbbb
	⇒ bbbbbbb

Reduce RHS:

[3]	bb(bba)
[3]	⇒ (bba)bb
	⇒ abbbb

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[7] bbbbbbbb=bbbb

Simplify [5] abbbbb=bbbb.

Reduce LHS:

[6]	(abbbb)b
	⇒ bbbbbbbb

Defines rule #1.