/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 N X Y Z)
(RULES
add(0,X) -> X
add(s(X),Y) -> s(add(X,Y))
dbl(0) -> 0
dbl(s(X)) -> s(s(dbl(X)))
first(0,X) -> nil
first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
sqr(0) -> 0
sqr(s(X)) -> s(add(sqr(X),dbl(X)))
terms(N) -> cons(recip(sqr(N)),terms(s(N)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ADD(s(X),Y) -> ADD(X,Y)
 DBL(s(X)) -> DBL(X)
 FIRST(s(X),cons(Y,Z)) -> FIRST(X,Z)
 SQR(s(X)) -> ADD(sqr(X),dbl(X))
 SQR(s(X)) -> DBL(X)
 SQR(s(X)) -> SQR(X)
 TERMS(N) -> SQR(N)
 TERMS(N) -> TERMS(s(N))
-> Rules:
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 dbl(0) -> 0
 dbl(s(X)) -> s(s(dbl(X)))
 first(0,X) -> nil
 first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
 sqr(0) -> 0
 sqr(s(X)) -> s(add(sqr(X),dbl(X)))
 terms(N) -> cons(recip(sqr(N)),terms(s(N)))

Problem 1: 

Infinite Processor:
-> Pairs:
 ADD(s(X),Y) -> ADD(X,Y)
 DBL(s(X)) -> DBL(X)
 FIRST(s(X),cons(Y,Z)) -> FIRST(X,Z)
 SQR(s(X)) -> ADD(sqr(X),dbl(X))
 SQR(s(X)) -> DBL(X)
 SQR(s(X)) -> SQR(X)
 TERMS(N) -> SQR(N)
 TERMS(N) -> TERMS(s(N))
-> Rules:
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 dbl(0) -> 0
 dbl(s(X)) -> s(s(dbl(X)))
 first(0,X) -> nil
 first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
 sqr(0) -> 0
 sqr(s(X)) -> s(add(sqr(X),dbl(X)))
 terms(N) -> cons(recip(sqr(N)),terms(s(N)))
-> Pairs in cycle:
 TERMS(N) -> TERMS(s(N))

The problem is infinite.