Certificate for #892 ⟨a, b | aaaabba=ba⟩

Back:⟨a, b | aaaabba=ba⟩

Completion settings:

[1] aaaabba=ba

Axiom: aaaabba=ba.

Referenced by [3].

[2] aaaabb=c

Axiom: aaaabb=c.

Defines rule #3.

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

[3] ba=ca

Overlap of [1] aaaabba=ba with [2] aaaabb=c:

aaaabba aaaabb

Critical pair: ca=ba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [5].

[4] aaaabca=ca

Overlap of [2] aaaabb=c with [3] ba=ca:

aaaab b ba

Critical pair: aaaabca=ca.

Referenced by [7].

[5] bc=cc

Overlap of [3] ba=ca with [2] aaaabb=c:

b a aaaabb

Critical pair: bc=caaaabb.

Reduce RHS:

[2]c(aaaabb)
⇒ cc

Defines rule #2.

Referenced by [6], [7].

[6] aaaaccc=cc

Overlap of [2] aaaabb=c with [5] bc=cc:

aaaab b bc

Critical pair: aaaabcc=cc.

Reduce LHS:

[5]aaaa(bc)c
⇒ aaaaccc

Defines rule #5.

[7] aaaacca=ca

Simplify [4] aaaabca=ca.

Reduce LHS:

[5]aaaa(bc)a
⇒ aaaacca

Defines rule #4.