Certificate for #3920 ⟨a, b | aaaababba=ab⟩

Completion settings:

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

Axiom: aaaababba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #4.

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

Overlap of [1] aaaababba=ab with [2] abb=c:

Critical pair: aaaabca=ab.

Defines rule #1.

Referenced by [4], [5], [6], [7], [10].

Overlap of [3] aaaabca=ab with [2] abb=c:

Critical pair: aaaabcc=abbb.

Reduce RHS:

Defines rule #3.

Referenced by [6], [7], [8], [12], [15].

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

Critical pair: aaaabcab=abaaabca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [7], [8], [9], [11], [13].

Overlap of [3] aaaabca=ab with [4] aaaabcc=cb:

Critical pair: aaaabccb=abaaabcc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [8], [9].

Overlap of [3] aaaabca=ab with [5] abaaabca=c:

Critical pair: aaaabcc=abbaaabca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11], [12], [13], [14], [16].

Overlap of [5] abaaabca=c with [4] aaaabcc=cb:

Critical pair: abaaabccb=caaabcc.

Reduce LHS:

Defines rule #11.

Referenced by [17].

Overlap of [5] abaaabca=c with [5] abaaabca=c:

Critical pair: abaaabcc=cbaaabca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [15], [16], [17].

Overlap of [3] aaaabca=ab with [7] caaabca=cb:

Critical pair: aaaabcb=abaabca.

Flip LHS and RHS.

Defines rule #5.

Referenced by [17].

Overlap of [5] abaaabca=c with [7] caaabca=cb:

Critical pair: abaaabcb=caabca.

Defines rule #12.

Overlap of [7] caaabca=cb with [4] aaaabcc=cb:

Critical pair: caaabccb=cbaaabcc.

Flip LHS and RHS.

Defines rule #10.

Referenced by [15].

Overlap of [7] caaabca=cb with [5] abaaabca=c:

Critical pair: caaabcc=cbbaaabca.

Flip LHS and RHS.

Defines rule #14.

Overlap of [7] caaabca=cb with [7] caaabca=cb:

Critical pair: caaabcb=cbaabca.

Flip LHS and RHS.

Defines rule #6.

Overlap of [9] cbaaabca=cbb with [4] aaaabcc=cb:

Critical pair: cbaaabccb=cbbaaabcc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Overlap of [9] cbaaabca=cbb with [7] caaabca=cb:

Critical pair: cbaaabcb=cbbaabca.

Flip LHS and RHS.

Defines rule #13.

Overlap of [9] cbaaabca=cbb with [10] abaabca=aaaabcb:

Critical pair: cbaaabcaaaabcb=cbbbaabca.

Reduce LHS:

Reduce RHS:

Defines rule #16.