Certificate for #7060 ⟨a, b, c | ab=1, bcbbc=c⟩

Completion settings:

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

[1] ab=1

Axiom: ab=1.

Defines rule #4.

Referenced by [3], [6].

[2] bcbbc=c

Axiom: bcbbc=c.

Referenced by [3], [4], [6], [7].

[3] ac=cbbc

Overlap of [1] ab=1 with [2] bcbbc=c:

a b bcbbc

Critical pair: ac=cbbc.

Referenced by [5].

[4] cbbc=bcbc

Overlap of [2] bcbbc=c with [2] bcbbc=c:

bcb bc bcbbc

Critical pair: bcbc=cbbc.

Flip LHS and RHS.

Referenced by [5], [6], [7], [9].

[5] ac=bcbc

Simplify [3] ac=cbbc.

Reduce RHS:

[4]	(cbbc)
	⇒ bcbc

Referenced by [6], [8].

[6] cbc=bcc

Overlap of [5] ac=bcbc with [4] cbbc=bcbc:

a c cbbc

Critical pair: abcbc=bcbcbbc.

Reduce LHS:

[1]	(ab)cbc
	⇒ cbc

Reduce RHS:

[2]	bc(bcbbc)
	⇒ bcc

Defines rule #1.

Referenced by [7], [8], [9].

[7] bbbcc=c

Overlap of [2] bcbbc=c with [4] cbbc=bcbc:

b cbbc cbbc

Critical pair: bbcbc=c.

Reduce LHS:

[6]	bb(cbc)
	⇒ bbbcc

Defines rule #3.

[8] ac=bbcc

Simplify [5] ac=bcbc.

Reduce RHS:

[6]	b(cbc)
	⇒ bbcc

Defines rule #5.

[9] cbbc=bbcc

Simplify [4] cbbc=bcbc.

Reduce RHS:

[6]	b(cbc)
	⇒ bbcc

Defines rule #2.