Certificate for #5240 ⟨a, b, c | aa=b, bbcb=c⟩

Back:⟨a, b, c | aa=b, bbcb=c⟩

Completion settings:

[1] b=aa

Axiom: aa=b.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2].

[2] aaaacaa=c

Axiom: bbcb=c.

Reduce LHS:

[1](b)bcb
[1]⇒ aa(b)cb
[1]⇒ aaaac(b)
⇒ aaaacaa

Defines rule #3.

Referenced by [3], [4].

[3] aaaacc=caacaa

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

aaaac aa aaaacaa

Critical pair: aaaacc=caacaa.

Defines rule #1.

[4] aaaacac=caaacaa

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

aaaaca a aaaacaa

Critical pair: aaaacac=caaacaa.

Defines rule #2.