Certificate for #4081 ⟨a, b | aabaaabba=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: aabaaabba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #4.

Referenced by [3], [4], [5], [7], [10].

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

Critical pair: aabaaca=ab.

Defines rule #1.

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

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

Critical pair: aabaacc=abbb.

Reduce RHS:

Defines rule #3.

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

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

Critical pair: aabaacab=ababaaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

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

Overlap of [3] aabaaca=ab with [4] aabaacc=cb:

Critical pair: aabaaccb=ababaacc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [8], [9].

Overlap of [3] aabaaca=ab with [5] ababaaca=c:

Critical pair: aabaacc=abbabaaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [5] ababaaca=c with [4] aabaacc=cb:

Critical pair: ababaaccb=cabaacc.

Reduce LHS:

Defines rule #11.

Referenced by [16].

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

Critical pair: ababaacc=cbabaaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

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

Overlap of [3] aabaaca=ab with [7] cabaaca=cb:

Critical pair: aabaacb=abbaaca.

Reduce RHS:

Defines rule #5.

Referenced by [17].

Overlap of [5] ababaaca=c with [7] cabaaca=cb:

Critical pair: ababaacb=cbaaca.

Defines rule #12.

Overlap of [7] cabaaca=cb with [4] aabaacc=cb:

Critical pair: cabaaccb=cbabaacc.

Flip LHS and RHS.

Defines rule #10.

Referenced by [15], [17].

Overlap of [7] cabaaca=cb with [5] ababaaca=c:

Critical pair: cabaacc=cbbabaaca.

Flip LHS and RHS.

Defines rule #14.

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

Critical pair: cabaacb=cbbaaca.

Flip LHS and RHS.

Defines rule #6.

Overlap of [9] cbabaaca=cbb with [4] aabaacc=cb:

Critical pair: cbabaaccb=cbbabaacc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Overlap of [9] cbabaaca=cbb with [7] cabaaca=cb:

Critical pair: cbabaacb=cbbbaaca.

Reduce RHS:

Defines rule #13.

Overlap of [9] cbabaaca=cbb with [10] aabaacb=caaca:

Critical pair: cbabaaccaaca=cbbabaacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #16.