Certificate for #2870 ⟨a, b | aaaabbaaaab=1⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = deg(d) = 1, a < d
• Auxiliary generators:
  1. aaaa=c
  2. bbaaaab=d

Axiom: aaaabbaaaab=1.

Referenced by [4].

Axiom: aaaa=c.

Defines rule #6.

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

Axiom: bbaaaab=d.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [1] aaaabbaaaab=1 with [2] aaaa=c:

Critical pair: cbbaaaab=1.

Reduce LHS:

Referenced by [5], [7].

Overlap of [4] cbbcb=1 with [4] cbbcb=1:

Critical pair: cbb=bcb.

Referenced by [7].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [4] cbbcb=1 with [5] cbb=bcb:

Critical pair: bcbcb=1.

Referenced by [8], [10].

Overlap of [7] bcbcb=1 with [7] bcbcb=1:

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [9], [10], [12], [13], [14].

Simplify [3] d=bbcb.

Reduce RHS:

Defines rule #5.

Overlap of [7] bcbcb=1 with [8] cb=bc:

Critical pair: bbccb=1.

Reduce LHS:

Defines rule #2.

Referenced by [11], [14].

Overlap of [10] bbbcc=1 with [6] ca=ac:

Critical pair: bbbcac=a.

Reduce LHS:

Referenced by [12].

Overlap of [11] bbbacc=a with [8] cb=bc:

Critical pair: bbbacbc=ab.

Reduce LHS:

Referenced by [13].

Overlap of [12] bbbabcc=ab with [8] cb=bc:

Critical pair: bbbabcbc=abb.

Reduce LHS:

Referenced by [14].

Overlap of [13] bbbabbcc=abb with [8] cb=bc:

Critical pair: bbbabbcbc=abbb.

Reduce LHS:

Defines rule #4.