Certificate for #5890 ⟨a, b | ababba=abbab⟩

Completion settings:

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

Axiom: ababba=abbab.

Referenced by [3].

Axiom: abbab=c.

Defines rule #11.

Referenced by [3], [4], [5], [6], [8], [9], [16].

Simplify [1] ababba=abbab.

Reduce RHS:

Defines rule #12.

Referenced by [5], [6], [12], [13].

Overlap of [2] abbab=c with [2] abbab=c:

Critical pair: abbc=cbab.

Flip LHS and RHS.

Referenced by [7].

Overlap of [3] ababba=c with [2] abbab=c:

Critical pair: abc=cb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8], [9], [10], [11], [12], [13], [15], [16].

Overlap of [2] abbab=c with [3] ababba=c:

Critical pair: abbc=cabba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [9], [10], [12], [15].

Simplify [4] cbab=abbc.

Reduce LHS:

Defines rule #6.

Referenced by [8], [9], [10], [11], [16].

Overlap of [2] abbab=c with [7] abcab=abbc:

Critical pair: abbabbc=ccab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [10], [11], [13], [15].

Overlap of [7] abcab=abbc with [6] cabba=abbc:

Critical pair: ababbc=abbcba.

Reduce RHS:

Defines rule #13.

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

Overlap of [8] ccab=abcc with [6] cabba=abbc:

Critical pair: cabbc=abccba.

Reduce RHS:

Defines rule #8.

Referenced by [16].

Overlap of [8] ccab=abcc with [9] ababbc=cca:

Critical pair: cccca=abccabbc.

Reduce RHS:

Defines rule #2.

Referenced by [14].

Overlap of [9] ababbc=cca with [6] cabba=abbc:

Critical pair: ababbabbc=ccaabba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [9] ababbc=cca with [8] ccab=abcc:

Critical pair: ababbabcc=ccacab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [9] ababbc=cca with [11] cccca=ccacc:

Critical pair: ababbccacc=ccaccca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [17].

Overlap of [13] ccacab=abccc with [6] cabba=abbc:

Critical pair: ccaabbc=abcccba.

Reduce RHS:

Defines rule #10.

Overlap of [7] abcab=abbc with [10] cabbc=abbcca:

Critical pair: ababbcca=abbcbc.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [17].

Simplify [14] ccaccca=ccacacc.

Reduce RHS:

Defines rule #3.