Certificate for #19803 ⟨a, b | aaa=a, aabb=bab⟩

Back:⟨a, b | aaa=a, aabb=bab⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #3.

Referenced by [6], [7].

[2] aabb=bab

Axiom: aabb=bab.

Referenced by [4].

[3] ab=c

Axiom: ab=c.

Defines rule #1.

Referenced by [4], [5], [6], [7], [8].

[4] aabb=bc

Simplify [2] aabb=bab.

Reduce RHS:

[3]b(ab)
⇒ bc

Referenced by [5].

[5] acb=bc

Overlap of [4] aabb=bc with [3] ab=c:

a abb ab

Critical pair: acb=bc.

Referenced by [7], [8].

[6] aac=c

Overlap of [1] aaa=a with [3] ab=c:

aa a ab

Critical pair: aac=ab.

Reduce RHS:

[3](ab)
⇒ c

Defines rule #4.

Referenced by [8].

[7] acc=bc

Overlap of [1] aaa=a with [5] acb=bc:

aa a acb

Critical pair: aabc=acb.

Reduce LHS:

[3]a(ab)c
⇒ acc

Reduce RHS:

[5](acb)
⇒ bc

Defines rule #5.

[8] cb=cc

Overlap of [6] aac=c with [5] acb=bc:

a ac acb

Critical pair: abc=cb.

Reduce LHS:

[3](ab)c
⇒ cc

Flip LHS and RHS.

Defines rule #2.