/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO

Problem 1: 

(VAR v_NonEmpty:S N:S X:S Y:S Z:S)
(RULES
2ndsneg(0,Z:S) -> rnil
2ndsneg(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,Z:S))
2ndspos(0,Z:S) -> rnil
2ndspos(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,Z:S))
from(X:S) -> cons(X:S,from(s(X:S)))
pi(X:S) -> 2ndspos(X:S,from(0))
plus(0,Y:S) -> Y:S
plus(s(X:S),Y:S) -> s(plus(X:S,Y:S))
square(X:S) -> times(X:S,X:S)
times(0,Y:S) -> 0
times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 2NDSNEG(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> 2NDSPOS(N:S,Z:S)
 2NDSPOS(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> 2NDSNEG(N:S,Z:S)
 FROM(X:S) -> FROM(s(X:S))
 PI(X:S) -> 2NDSPOS(X:S,from(0))
 PI(X:S) -> FROM(0)
 PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S)
 SQUARE(X:S) -> TIMES(X:S,X:S)
 TIMES(s(X:S),Y:S) -> PLUS(Y:S,times(X:S,Y:S))
 TIMES(s(X:S),Y:S) -> TIMES(X:S,Y:S)
-> Rules:
 2ndsneg(0,Z:S) -> rnil
 2ndsneg(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,Z:S))
 2ndspos(0,Z:S) -> rnil
 2ndspos(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,Z:S))
 from(X:S) -> cons(X:S,from(s(X:S)))
 pi(X:S) -> 2ndspos(X:S,from(0))
 plus(0,Y:S) -> Y:S
 plus(s(X:S),Y:S) -> s(plus(X:S,Y:S))
 square(X:S) -> times(X:S,X:S)
 times(0,Y:S) -> 0
 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S))

Problem 1: 

Infinite Processor:
-> Pairs:
 2NDSNEG(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> 2NDSPOS(N:S,Z:S)
 2NDSPOS(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> 2NDSNEG(N:S,Z:S)
 FROM(X:S) -> FROM(s(X:S))
 PI(X:S) -> 2NDSPOS(X:S,from(0))
 PI(X:S) -> FROM(0)
 PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S)
 SQUARE(X:S) -> TIMES(X:S,X:S)
 TIMES(s(X:S),Y:S) -> PLUS(Y:S,times(X:S,Y:S))
 TIMES(s(X:S),Y:S) -> TIMES(X:S,Y:S)
-> Rules:
 2ndsneg(0,Z:S) -> rnil
 2ndsneg(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,Z:S))
 2ndspos(0,Z:S) -> rnil
 2ndspos(s(N:S),cons(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,Z:S))
 from(X:S) -> cons(X:S,from(s(X:S)))
 pi(X:S) -> 2ndspos(X:S,from(0))
 plus(0,Y:S) -> Y:S
 plus(s(X:S),Y:S) -> s(plus(X:S,Y:S))
 square(X:S) -> times(X:S,X:S)
 times(0,Y:S) -> 0
 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S))
-> Pairs in cycle:
 FROM(X:S) -> FROM(s(X:S))

The problem is infinite.