Certificate for #4815 ⟨a, b | ababaaab=baa⟩

Completion settings:

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

Axiom: ababaaab=baa.

Referenced by [3].

Axiom: abaa=c.

Referenced by [3], [4].

Overlap of [1] ababaaab=baa with [2] abaa=c:

Critical pair: abcab=baa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5], [6], [7], [17], [18].

Overlap of [2] abaa=c with [3] baa=abcab:

Critical pair: aabcab=c.

Defines rule #7.

Referenced by [5], [6], [7], [8], [9], [10], [11], [12], [17], [18].

Overlap of [3] baa=abcab with [4] aabcab=c:

Critical pair: bc=abcabbcab.

Flip LHS and RHS.

Defines rule #8.

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

Overlap of [3] baa=abcab with [4] aabcab=c:

Critical pair: bac=abcababcab.

Flip LHS and RHS.

Defines rule #13.

Referenced by [10], [11], [14].

Overlap of [4] aabcab=c with [3] baa=abcab:

Critical pair: aabcaabcab=caa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] aabcab=c with [5] abcabbcab=bc:

Critical pair: abc=cbcab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [15], [17], [18].

Overlap of [4] aabcab=c with [5] abcabbcab=bc:

Critical pair: aabcbc=ccabbcab.

Flip LHS and RHS.

Defines rule #6.

Overlap of [4] aabcab=c with [6] abcababcab=bac:

Critical pair: abac=cabcab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [12], [13], [14], [15], [16].

Overlap of [4] aabcab=c with [6] abcababcab=bac:

Critical pair: aabcbac=ccababcab.

Flip LHS and RHS.

Defines rule #10.

Overlap of [4] aabcab=c with [10] cabcab=abac:

Critical pair: aababac=ccab.

Defines rule #12.

Referenced by [17], [18].

Overlap of [5] abcabbcab=bc with [10] cabcab=abac:

Critical pair: abcabbabac=bccab.

Defines rule #14.

Overlap of [6] abcababcab=bac with [10] cabcab=abac:

Critical pair: abcabababac=baccab.

Defines rule #16.

Overlap of [8] cbcab=abc with [10] cabcab=abac:

Critical pair: cbabac=abccab.

Defines rule #5.

Referenced by [17].

Overlap of [10] cabcab=abac with [10] cabcab=abac:

Critical pair: cababac=abaccab.

Defines rule #9.

Referenced by [18].

Overlap of [12] aababac=ccab with [15] cbabac=abccab:

Critical pair: aababaabccab=ccabbabac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [12] aababac=ccab with [16] cababac=abaccab:

Critical pair: aababaabaccab=ccabababac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.