Certificate for #2184 ⟨a, b, c | aabb=1, bcbc=1⟩

Completion settings:

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

Axiom: aabb=1.

Referenced by [3], [4].

Axiom: bcbc=1.

Defines rule #1.

Referenced by [3], [5], [7], [8].

Overlap of [1] aabb=1 with [2] bcbc=1:

Critical pair: aab=cbc.

Referenced by [4], [5].

Overlap of [1] aabb=1 with [3] aab=cbc:

Critical pair: cbcb=1.

Defines rule #2.

Referenced by [9], [10].

Overlap of [3] aab=cbc with [2] bcbc=1:

Critical pair: aa=cbccbc.

Defines rule #5.

Referenced by [6].

Overlap of [5] aa=cbccbc with [5] aa=cbccbc:

Critical pair: acbccbc=cbccbca.

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] bcbc=1 with [6] cbccbca=acbccbc:

Critical pair: bacbccbc=cbca.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8].

Overlap of [2] bcbc=1 with [7] cbca=bacbccbc:

Critical pair: bbacbccbc=a.

Referenced by [9].

Overlap of [8] bbacbccbc=a with [4] cbcb=1:

Critical pair: bbacbc=ab.

Referenced by [10].

Overlap of [9] bbacbc=ab with [4] cbcb=1:

Critical pair: bba=abb.

Defines rule #3.