Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-2-num-20)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by AProVE @ termCOMP 2023)

1 Looping derivation

There is a looping derivation.

a a b a b a b a b a b a b →⁺ ε a a b a b a b a b a b a b a

The derivation can be derived as follows.

• a a b →⁺ b a b a: This is an original rule (OC1).
• a →⁺ ε: This is an original rule (OC1).
• a a b →⁺ b b a: The overlap closure is obtained from the following two overlap closures (OC3).
  • a a b →⁺ b a b a
  • a →⁺ ε
• a a b a b →⁺ b b b a b a: The overlap closure is obtained from the following two overlap closures (OC2).
  • a a b →⁺ b b a
  • a a b →⁺ b a b a
• b b b →⁺ a: This is an original rule (OC1).
• a a b a b →⁺ a a b a: The overlap closure is obtained from the following two overlap closures (OC3).
  • a a b a b →⁺ b b b a b a
  • b b b →⁺ a
• a a b a b →⁺ b a b b b a: The overlap closure is obtained from the following two overlap closures (OC2).
  • a a b →⁺ b a b a
  • a a b →⁺ b b a
• a a b a b →⁺ b a a a: The overlap closure is obtained from the following two overlap closures (OC3).
  • a a b a b →⁺ b a b b b a
  • b b b →⁺ a
• a a b a b a b a b →⁺ a a b b a a a: The overlap closure is obtained from the following two overlap closures (OC2).
  • a a b a b →⁺ a a b a
  • a a b a b →⁺ b a a a
• a a b a b a b a b a b →⁺ a a b b a a b a b a: The overlap closure is obtained from the following two overlap closures (OC2).
  • a a b a b a b a b →⁺ a a b b a a a
  • a a b →⁺ b a b a
• a a b a b a b a b a b →⁺ a a b b b a b a a b a: The overlap closure is obtained from the following two overlap closures (OC3).
  • a a b a b a b a b a b →⁺ a a b b a a b a b a
  • a a b →⁺ b a b a
• a a b a b a b a b a b →⁺ a a a a b a a b a: The overlap closure is obtained from the following two overlap closures (OC3).
  • a a b a b a b a b a b →⁺ a a b b b a b a a b a
  • b b b →⁺ a
• a a b a b a b a b a b →⁺ a a b a b a a a b a: The overlap closure is obtained from the following two overlap closures (OC3).
  • a a b a b a b a b a b →⁺ a a a a b a a b a
  • a a b →⁺ b a b a
• a a b a b a b a b a b →⁺ a a b a b a b a b a a: The overlap closure is obtained from the following two overlap closures (OC3).
  • a a b a b a b a b a b →⁺ a a b a b a a a b a
  • a a b →⁺ b a b a
• a a b a b a b a b a b a b →⁺ a a b a b a b a b a b a b a: The overlap closure is obtained from the following two overlap closures (OC2).
  • a a b a b a b a b a b →⁺ a a b a b a b a b a a
  • a a b →⁺ b a b a