Certificate for #25209 ⟨a, b | aa=a, abbba=abb⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #1.

Referenced by [4], [7].

Axiom: abbba=abb.

Defines rule #8.

Referenced by [4], [5], [6], [8], [11], [12], [13].

Axiom: abbbbbbbb=c.

Defines rule #16.

Referenced by [7], [8], [9], [14], [16], [17].

Overlap of [2] abbba=abb with [1] aa=a:

Critical pair: abbba=abba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [6], [9], [17].

Overlap of [2] abbba=abb with [2] abbba=abb:

Critical pair: abbbabb=abbbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Referenced by [16].

Overlap of [2] abbba=abb with [4] abba=abb:

Critical pair: abbbabb=abbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [12], [13], [14], [15], [17].

Overlap of [1] aa=a with [3] abbbbbbbb=c:

Critical pair: ac=abbbbbbbb.

Reduce RHS:

Defines rule #2.

Overlap of [2] abbba=abb with [3] abbbbbbbb=c:

Critical pair: abbbc=abbbbbbbbbb.

Reduce RHS:

Referenced by [10].

Overlap of [4] abba=abb with [3] abbbbbbbb=c:

Critical pair: abbc=abbbbbbbbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [10], [17].

Simplify [8] abbbc=cbb.

Reduce RHS:

Defines rule #9.

Referenced by [11], [15].

Overlap of [2] abbba=abb with [10] abbbc=abbc:

Critical pair: abbbabbc=abbbbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Overlap of [2] abbba=abb with [6] abbbba=abbbb:

Critical pair: abbbabbbb=abbbbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Referenced by [17].

Overlap of [6] abbbba=abbbb with [2] abbba=abb:

Critical pair: abbbbabb=abbbbbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [6] abbbba=abbbb with [6] abbbba=abbbb:

Critical pair: abbbbabbbb=abbbbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] abbbba=abbbb with [10] abbbc=abbc:

Critical pair: abbbbabbc=abbbbbbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Overlap of [5] abbbbba=abbbb with [5] abbbbba=abbbb:

Critical pair: abbbbbabbbb=abbbbbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [17].

Overlap of [16] cba=c with [3] abbbbbbbb=c:

Critical pair: cbc=cbbbbbbbb.

Reduce RHS:

Defines rule #5.