Certificate for #3040 ⟨a, b, c | aba=b, bcb=c⟩

Completion settings:

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

Axiom: aba=b.

Defines rule #8.

Referenced by [4], [5].

Axiom: bcb=c.

Defines rule #9.

Referenced by [9], [10], [11], [13].

Axiom: abb=d.

Defines rule #2.

Referenced by [4], [5], [6], [7], [8], [11], [12].

Overlap of [1] aba=b with [1] aba=b:

Critical pair: abb=bba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [8], [10].

Overlap of [1] aba=b with [3] abb=d:

Critical pair: abd=bbb.

Defines rule #7.

Referenced by [7], [12].

Overlap of [3] abb=d with [4] bba=d:

Critical pair: ad=da.

Defines rule #6.

Overlap of [3] abb=d with [4] bba=d:

Critical pair: abd=dba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [4] bba=d with [3] abb=d:

Critical pair: bbd=dbb.

Defines rule #1.

Referenced by [12].

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

Critical pair: bcc=ccb.

Defines rule #13.

Overlap of [2] bcb=c with [4] bba=d:

Critical pair: bcd=cba.

Defines rule #10.

Overlap of [3] abb=d with [2] bcb=c:

Critical pair: abc=dcb.

Defines rule #12.

Referenced by [13].

Overlap of [3] abb=d with [8] bbd=dbb:

Critical pair: abdbb=dbd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [11] abc=dcb with [2] bcb=c:

Critical pair: ac=dcbb.

Defines rule #11.