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TRS Stand 20472 pair #381716197
details
property
value
status
complete
benchmark
ExIntrod_GM99_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n192.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
23.4441719055 seconds
cpu usage
89.755388177
max memory
7.593271296E9
stage attributes
key
value
output-size
84974
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 24 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 227 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 246 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 213 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) QDP (15) QDPOrderProof [EQUIVALENT, 196 ms] (16) QDP (17) QDPOrderProof [EQUIVALENT, 46 ms] (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 219 ms] (22) QDP (23) QDPOrderProof [EQUIVALENT, 215 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) QDP (27) QDPOrderProof [EQUIVALENT, 211 ms] (28) QDP (29) DependencyGraphProof [EQUIVALENT, 0 ms] (30) QDP (31) QDPOrderProof [EQUIVALENT, 221 ms] (32) QDP (33) QDPOrderProof [EQUIVALENT, 199 ms] (34) QDP (35) QDPOrderProof [EQUIVALENT, 158 ms] (36) QDP (37) QDPOrderProof [EQUIVALENT, 76 ms] (38) QDP (39) DependencyGraphProof [EQUIVALENT, 0 ms] (40) QDP (41) QDPSizeChangeProof [EQUIVALENT, 0 ms] (42) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__primes -> a__sieve(a__from(s(s(0)))) a__from(X) -> cons(mark(X), from(s(X))) a__head(cons(X, Y)) -> mark(X) a__tail(cons(X, Y)) -> mark(Y) a__if(true, X, Y) -> mark(X) a__if(false, X, Y) -> mark(Y) a__filter(s(s(X)), cons(Y, Z)) -> a__if(divides(s(s(mark(X))), mark(Y)), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y))) mark(primes) -> a__primes mark(sieve(X)) -> a__sieve(mark(X)) mark(from(X)) -> a__from(mark(X)) mark(head(X)) -> a__head(mark(X)) mark(tail(X)) -> a__tail(mark(X)) mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2)) mark(s(X)) -> s(mark(X)) mark(0) -> 0 mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(true) -> true mark(false) -> false mark(divides(X1, X2)) -> divides(mark(X1), mark(X2)) a__primes -> primes a__sieve(X) -> sieve(X) a__from(X) -> from(X) a__head(X) -> head(X) a__tail(X) -> tail(X) a__if(X1, X2, X3) -> if(X1, X2, X3) a__filter(X1, X2) -> filter(X1, X2) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
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