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TRS Standard pair #516963475
details
property
value
status
complete
benchmark
ExIntrod_GM99_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n085.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
6.54755496979 seconds
cpu usage
19.157936486
max memory
1.212166144E9
stage attributes
key
value
output-size
22706
starexec-result
NO
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 17 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 78 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) TransformationProof [EQUIVALENT, 0 ms] (11) QDP (12) TransformationProof [EQUIVALENT, 0 ms] (13) QDP (14) DependencyGraphProof [EQUIVALENT, 0 ms] (15) QDP (16) TransformationProof [EQUIVALENT, 0 ms] (17) QDP (18) DependencyGraphProof [EQUIVALENT, 0 ms] (19) QDP (20) QDPOrderProof [EQUIVALENT, 0 ms] (21) QDP (22) QDPOrderProof [EQUIVALENT, 0 ms] (23) QDP (24) NonTerminationLoopProof [COMPLETE, 0 ms] (25) NO (26) QDP (27) UsableRulesProof [EQUIVALENT, 0 ms] (28) QDP (29) QDPSizeChangeProof [EQUIVALENT, 0 ms] (30) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: primes -> sieve(from(s(s(0)))) from(X) -> cons(X, n__from(s(X))) head(cons(X, Y)) -> X tail(cons(X, Y)) -> activate(Y) if(true, X, Y) -> activate(X) if(false, X, Y) -> activate(Y) filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), n__filter(s(s(X)), activate(Z)), n__cons(Y, n__filter(X, sieve(Y)))) sieve(cons(X, Y)) -> cons(X, n__filter(X, sieve(activate(Y)))) from(X) -> n__from(X) filter(X1, X2) -> n__filter(X1, X2) cons(X1, X2) -> n__cons(X1, X2) activate(n__from(X)) -> from(X) activate(n__filter(X1, X2)) -> filter(X1, X2) activate(n__cons(X1, X2)) -> cons(X1, X2) activate(X) -> X Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: PRIMES -> SIEVE(from(s(s(0)))) PRIMES -> FROM(s(s(0))) FROM(X) -> CONS(X, n__from(s(X))) TAIL(cons(X, Y)) -> ACTIVATE(Y) IF(true, X, Y) -> ACTIVATE(X) IF(false, X, Y) -> ACTIVATE(Y) FILTER(s(s(X)), cons(Y, Z)) -> IF(divides(s(s(X)), Y), n__filter(s(s(X)), activate(Z)), n__cons(Y, n__filter(X, sieve(Y)))) FILTER(s(s(X)), cons(Y, Z)) -> ACTIVATE(Z) FILTER(s(s(X)), cons(Y, Z)) -> SIEVE(Y) SIEVE(cons(X, Y)) -> CONS(X, n__filter(X, sieve(activate(Y)))) SIEVE(cons(X, Y)) -> SIEVE(activate(Y)) SIEVE(cons(X, Y)) -> ACTIVATE(Y) ACTIVATE(n__from(X)) -> FROM(X) ACTIVATE(n__filter(X1, X2)) -> FILTER(X1, X2) ACTIVATE(n__cons(X1, X2)) -> CONS(X1, X2) The TRS R consists of the following rules:
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