Certificate for #1441 ⟨a, b | aabbaaabba=1⟩

Completion settings:

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

Axiom: aabbaaabba=1.

Referenced by [4].

Axiom: aaa=c.

Defines rule #6.

Referenced by [3], [4], [5], [6], [7].

Axiom: bbaaabb=d.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [1] aabbaaabba=1 with [2] aaa=c:

Critical pair: aabbcbba=1.

Referenced by [6], [7], [8], [9], [10].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [12].

Overlap of [2] aaa=c with [4] aabbcbba=1:

Critical pair: a=cbbcbba.

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] aabbcbba=1 with [2] aaa=c:

Critical pair: aabbcbbc=aa.

Referenced by [9].

Overlap of [6] cbbcbba=a with [4] aabbcbba=1:

Critical pair: cbbcbb=aabbcbba.

Reduce RHS:

Referenced by [11], [13].

Overlap of [4] aabbcbba=1 with [7] aabbcbbc=aa:

Critical pair: aabbcbbaa=abbcbbc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [4] aabbcbba=1 with [9] abbcbbc=a:

Critical pair: aabbcbba=bbcbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11], [12].

Overlap of [8] cbbcbb=1 with [10] bbcbbc=1:

Critical pair: cbbcb=bcbbc.

Defines rule #1.

Overlap of [10] bbcbbc=1 with [5] ca=ac:

Critical pair: bbcbbac=a.

Referenced by [13].

Overlap of [12] bbcbbac=a with [8] cbbcbb=1:

Critical pair: bbcbba=abbcbb.

Defines rule #4.