Certificate for #1648 ⟨a, b | aab=bb, abb=a⟩

Completion settings:

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

[1] bb=aab

Axiom: aab=bb.

Flip LHS and RHS.

Referenced by [2], [3], [4], [6], [9].

[2] aaab=a

Axiom: abb=a.

Reduce LHS:

[1]	a(bb)
	⇒ aaab

Referenced by [3], [4], [7].

[3] baab=aa

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

b b bb

Critical pair: baab=aabb.

Reduce RHS:

[1]	aa(bb)
[2]	⇒ a(aaab)
	⇒ aa

Referenced by [5].

[4] ab=aaa

Overlap of [2] aaab=a with [1] bb=aab:

aaa b bb

Critical pair: aaaaab=ab.

Reduce LHS:

[2]	aa(aaab)
	⇒ aaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [9].

[5] baaaa=aa

Simplify [3] baab=aa.

Reduce LHS:

[4]	ba(ab)
	⇒ baaaa

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

[6] baa=aaaa

Overlap of [1] bb=aab with [5] baaaa=aa:

b b baaaa

Critical pair: baa=aabaaaa.

Reduce RHS:

[5]	aa(baaaa)
	⇒ aaaa

Referenced by [7].

[7] aaaaa=a

Overlap of [5] baaaa=aa with [2] aaab=a:

baa aa aaab

Critical pair: baaa=aaab.

Reduce LHS:

[6]	(baa)a
	⇒ aaaaa

Reduce RHS:

[2]	(aaab)
	⇒ a

Defines rule #1.

Referenced by [8].

[8] ba=aaa

Overlap of [5] baaaa=aa with [7] aaaaa=a:

b aaaa aaaaa

Critical pair: ba=aaa.

Defines rule #2.

[9] bb=aaaa

Simplify [1] bb=aab.

Reduce RHS:

[4]	a(ab)
	⇒ aaaa

Defines rule #4.