Certificate for #575 ⟨a, b | abba=abab⟩

Completion settings:

• Auxiliary generators:
  1. c = abbab
• Reduction order:
  • Left-to-right shortlex with b < a < c

Axiom: abba=abab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [4], [5], [6], [7], [10], [12].

Axiom: abbab=c.

Defines rule #10.

Referenced by [3], [4], [5], [6], [7], [9], [12].

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

Critical pair: abbc=cbab.

Flip LHS and RHS.

Referenced by [8].

Overlap of [1] abab=abba with [1] abab=abba:

Critical pair: ababba=abbaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

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

Overlap of [1] abab=abba with [2] abbab=c:

Critical pair: abc=abbabab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6], [7], [11], [13], [14].

Overlap of [2] abbab=c with [1] abab=abba:

Critical pair: abbabba=cab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [7], [8], [10], [11].

Overlap of [5] cab=abc with [2] abbab=c:

Critical pair: cc=abcbab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #13.

Simplify [3] cbab=abbc.

Reduce LHS:

Defines rule #6.

Referenced by [9], [10], [13], [14].

Overlap of [2] abbab=c with [8] abcb=abbc:

Critical pair: abbabbc=ccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [8] abcb=abbc with [6] cba=abc:

Critical pair: ababc=abbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Referenced by [14].

Overlap of [9] ccb=cbc with [6] cba=abc:

Critical pair: cabc=cbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [1] abab=abba with [4] abbaab=ca:

Critical pair: abca=abbabaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [4] abbaab=ca with [8] abcb=abbc:

Critical pair: abbaabbc=cacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [5] cab=abc with [4] abbaab=ca:

Critical pair: cca=abcbaab.

Reduce RHS:

Defines rule #4.