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


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YES

Problem 1: 

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

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 add(0,X) -> X
 add(s,Y) -> s
 dbl(0) -> 0
 dbl(s) -> s
 first(0,X) -> nil
 first(s,cons(Y)) -> cons(Y)
 sqr(0) -> 0
 sqr(s) -> s
 terms(N) -> cons(recip(sqr(N)))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 TERMS(N) -> SQR(N)
-> Rules:
 add(0,X) -> X
 add(s,Y) -> s
 dbl(0) -> 0
 dbl(s) -> s
 first(0,X) -> nil
 first(s,cons(Y)) -> cons(Y)
 sqr(0) -> 0
 sqr(s) -> s
 terms(N) -> cons(recip(sqr(N)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.