Certificate for #4319 ⟨a, b | ababbbaba=ab⟩

Completion settings:

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

Axiom: ababbbaba=ab.

Referenced by [3].

Axiom: abbb=c.

Defines rule #6.

Referenced by [3], [4], [11], [14], [15].

Overlap of [1] ababbbaba=ab with [2] abbb=c:

Critical pair: abcaba=ab.

Defines rule #11.

Referenced by [4], [5], [6], [7], [9], [10], [11], [14].

Overlap of [3] abcaba=ab with [2] abbb=c:

Critical pair: abcabc=abbbb.

Reduce RHS:

Defines rule #5.

Referenced by [6], [7], [8], [9], [10], [11], [12].

Overlap of [3] abcaba=ab with [3] abcaba=ab:

Critical pair: abcabab=abbcaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Referenced by [14], [15].

Overlap of [3] abcaba=ab with [4] abcabc=cb:

Critical pair: abcabcb=abbcabc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Referenced by [11], [13], [16].

Overlap of [4] abcabc=cb with [3] abcaba=ab:

Critical pair: abcab=cbaba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [10].

Overlap of [4] abcabc=cb with [4] abcabc=cb:

Critical pair: abccb=cbabc.

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [4] abcabc=cb with [8] cbabc=abccb:

Critical pair: abcababccb=cbbabc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [4] abcabc=cb with [7] cbaba=abcab:

Critical pair: abcababcab=cbbaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Overlap of [3] abcaba=ab with [6] abbcabc=cbb:

Critical pair: abcabcbb=abbbcabc.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Referenced by [12], [13].

Overlap of [4] abcabc=cb with [11] cbbb=ccabc:

Critical pair: abcabccabc=cbbbb.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Overlap of [6] abbcabc=cbb with [11] cbbb=ccabc:

Critical pair: abbcabccabc=cbbbbb.

Reduce LHS:

Reduce RHS:

Defines rule #10.

Overlap of [3] abcaba=ab with [5] abbcaba=abb:

Critical pair: abcababb=abbbcaba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [16].

Overlap of [5] abbcaba=abb with [5] abbcaba=abb:

Critical pair: abbcababb=abbbbcaba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] abbcabc=cbb with [14] ccaba=c:

Critical pair: abbcabc=cbbcaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.