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TRS Inner 89993 pair #381733829
details
property
value
status
complete
benchmark
Ex9_BLR02_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n014.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.81780290604 seconds
cpu usage
4.184935621
max memory
2.10485248E8
stage attributes
key
value
output-size
11247
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [SOUND, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 34 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 7 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 0 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 0 ms] (10) CSR (11) RisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(filter(cons(X, Y), 0, M)) -> mark(cons(0, filter(Y, M, M))) active(filter(cons(X, Y), s(N), M)) -> mark(cons(X, filter(Y, N, M))) active(sieve(cons(0, Y))) -> mark(cons(0, sieve(Y))) active(sieve(cons(s(N), Y))) -> mark(cons(s(N), sieve(filter(Y, N, N)))) active(nats(N)) -> mark(cons(N, nats(s(N)))) active(zprimes) -> mark(sieve(nats(s(s(0))))) active(filter(X1, X2, X3)) -> filter(active(X1), X2, X3) active(filter(X1, X2, X3)) -> filter(X1, active(X2), X3) active(filter(X1, X2, X3)) -> filter(X1, X2, active(X3)) active(cons(X1, X2)) -> cons(active(X1), X2) active(s(X)) -> s(active(X)) active(sieve(X)) -> sieve(active(X)) active(nats(X)) -> nats(active(X)) filter(mark(X1), X2, X3) -> mark(filter(X1, X2, X3)) filter(X1, mark(X2), X3) -> mark(filter(X1, X2, X3)) filter(X1, X2, mark(X3)) -> mark(filter(X1, X2, X3)) cons(mark(X1), X2) -> mark(cons(X1, X2)) s(mark(X)) -> mark(s(X)) sieve(mark(X)) -> mark(sieve(X)) nats(mark(X)) -> mark(nats(X)) proper(filter(X1, X2, X3)) -> filter(proper(X1), proper(X2), proper(X3)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(sieve(X)) -> sieve(proper(X)) proper(nats(X)) -> nats(proper(X)) proper(zprimes) -> ok(zprimes) filter(ok(X1), ok(X2), ok(X3)) -> ok(filter(X1, X2, X3)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) s(ok(X)) -> ok(s(X)) sieve(ok(X)) -> ok(sieve(X)) nats(ok(X)) -> ok(nats(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) The set Q consists of the following terms: active(nats(x0)) active(zprimes) active(filter(x0, x1, x2)) active(cons(x0, x1)) active(s(x0)) active(sieve(x0)) filter(mark(x0), x1, x2) filter(x0, mark(x1), x2) filter(x0, x1, mark(x2)) cons(mark(x0), x1) s(mark(x0)) sieve(mark(x0)) nats(mark(x0)) proper(filter(x0, x1, x2)) proper(cons(x0, x1)) proper(0) proper(s(x0)) proper(sieve(x0)) proper(nats(x0)) proper(zprimes) filter(ok(x0), ok(x1), ok(x2)) cons(ok(x0), ok(x1)) s(ok(x0)) sieve(ok(x0)) nats(ok(x0)) top(mark(x0)) top(ok(x0))
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