Certificate for #20217 ⟨a, b | aba=a, abba=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: aba=a.

Defines rule #2.

Referenced by [4], [7], [15].

Axiom: abba=abb.

Defines rule #6.

Referenced by [4], [5], [6], [8], [10], [11].

Axiom: abbbbbbbb=c.

Defines rule #16.

Referenced by [7], [8], [9], [13].

Overlap of [2] abba=abb with [1] aba=a:

Critical pair: abba=abbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [6], [9], [12].

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

Critical pair: abbabb=abbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [11], [12], [13], [14].

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

Critical pair: abbabb=abbbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

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

Critical pair: abc=abbbbbbbb.

Reduce RHS:

Defines rule #3.

Referenced by [16].

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

Critical pair: abbc=abbbbbbbbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [9].

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

Critical pair: abbbc=abbbbbbbbbb.

Reduce RHS:

Defines rule #9.

Referenced by [10], [14].

Overlap of [2] abba=abb with [9] abbbc=abbc:

Critical pair: abbabbc=abbbbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Overlap of [2] abba=abb with [5] abbbba=abbbb:

Critical pair: abbabbbb=abbbbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Overlap of [5] abbbba=abbbb with [4] abbba=abb:

Critical pair: abbbbabb=abbbbbbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

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

Critical pair: abbbbabbbb=abbbbbbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [15], [16].

Overlap of [5] abbbba=abbbb with [9] abbbc=abbc:

Critical pair: abbbbabbc=abbbbbbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Overlap of [13] ca=c with [1] aba=a:

Critical pair: ca=cba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [13] ca=c with [7] abc=c:

Critical pair: cc=cbc.

Flip LHS and RHS.

Defines rule #5.