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


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NO

Problem 1: 

(VAR v_NonEmpty:S L:S X:S)
(RULES
adx(cons(X:S,L:S)) -> incr(cons(X:S,adx(L:S)))
adx(nil) -> nil
head(cons(X:S,L:S)) -> X:S
incr(cons(X:S,L:S)) -> cons(s(X:S),incr(L:S))
incr(nil) -> nil
nats -> adx(zeros)
tail(cons(X:S,L:S)) -> L:S
zeros -> cons(0,zeros)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ADX(cons(X:S,L:S)) -> ADX(L:S)
 ADX(cons(X:S,L:S)) -> INCR(cons(X:S,adx(L:S)))
 INCR(cons(X:S,L:S)) -> INCR(L:S)
 NATS -> ADX(zeros)
 NATS -> ZEROS
 ZEROS -> ZEROS
-> Rules:
 adx(cons(X:S,L:S)) -> incr(cons(X:S,adx(L:S)))
 adx(nil) -> nil
 head(cons(X:S,L:S)) -> X:S
 incr(cons(X:S,L:S)) -> cons(s(X:S),incr(L:S))
 incr(nil) -> nil
 nats -> adx(zeros)
 tail(cons(X:S,L:S)) -> L:S
 zeros -> cons(0,zeros)

Problem 1: 

Infinite Processor:
-> Pairs:
 ADX(cons(X:S,L:S)) -> ADX(L:S)
 ADX(cons(X:S,L:S)) -> INCR(cons(X:S,adx(L:S)))
 INCR(cons(X:S,L:S)) -> INCR(L:S)
 NATS -> ADX(zeros)
 NATS -> ZEROS
 ZEROS -> ZEROS
-> Rules:
 adx(cons(X:S,L:S)) -> incr(cons(X:S,adx(L:S)))
 adx(nil) -> nil
 head(cons(X:S,L:S)) -> X:S
 incr(cons(X:S,L:S)) -> cons(s(X:S),incr(L:S))
 incr(nil) -> nil
 nats -> adx(zeros)
 tail(cons(X:S,L:S)) -> L:S
 zeros -> cons(0,zeros)
-> Pairs in cycle:
 ZEROS -> ZEROS

The problem is infinite.