Certification Problem

Input (TPDB TRS_Outermost/Strategy_outermost_added_08/2.05)

The rewrite relation of the following TRS is considered.

+(x,+(y,z))	→	+(+(x,y),z)	(1)
*(x,+(y,z))	→	+((x,y),(x,z))	(2)
+(+(x,(y,z)),(y,u))	→	+(x,*(y,+(z,u)))	(3)

The evaluation strategy is outermost

Property / Task

Prove or disprove termination.

Answer / Result

No.

Proof (by AProVE @ termCOMP 2023)

1 Loop

The following loop proves nontermination.

t₀	=	+(+(x'',(y,z)),(y,u))
	→	+(x'',*(y,+(z,u)))
	→	+(x'',+((y,z),(y,u)))
	→	+(+(x'',(y,z)),(y,u))
	=	t₃

where t₃ = t₀