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TRS Stand 20472 pair #381715792
details
property
value
status
complete
benchmark
Ex1_2_AEL03_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.82348394394 seconds
cpu usage
4.164522973
max memory
2.2298624E8
stage attributes
key
value
output-size
25346
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRInnermostProof [EQUIVALENT, 6 ms] (4) CSR (5) CSDependencyPairsProof [EQUIVALENT, 0 ms] (6) QCSDP (7) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QCSDP (10) QCSDPSubtermProof [EQUIVALENT, 0 ms] (11) QCSDP (12) PIsEmptyProof [EQUIVALENT, 0 ms] (13) YES (14) QCSDP (15) QCSDPSubtermProof [EQUIVALENT, 0 ms] (16) QCSDP (17) PIsEmptyProof [EQUIVALENT, 0 ms] (18) YES (19) QCSDP (20) QCSDPSubtermProof [EQUIVALENT, 0 ms] (21) QCSDP (22) PIsEmptyProof [EQUIVALENT, 0 ms] (23) YES (24) QCSDP (25) QCSDPSubtermProof [EQUIVALENT, 0 ms] (26) QCSDP (27) PIsEmptyProof [EQUIVALENT, 0 ms] (28) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(from(X)) -> mark(cons(X, from(s(X)))) active(2ndspos(0, Z)) -> mark(rnil) active(2ndspos(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(posrecip(Y), 2ndsneg(N, Z))) active(2ndsneg(0, Z)) -> mark(rnil) active(2ndsneg(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(negrecip(Y), 2ndspos(N, Z))) active(pi(X)) -> mark(2ndspos(X, from(0))) active(plus(0, Y)) -> mark(Y) active(plus(s(X), Y)) -> mark(s(plus(X, Y))) active(times(0, Y)) -> mark(0) active(times(s(X), Y)) -> mark(plus(Y, times(X, Y))) active(square(X)) -> mark(times(X, X)) active(s(X)) -> s(active(X)) active(posrecip(X)) -> posrecip(active(X)) active(negrecip(X)) -> negrecip(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(rcons(X1, X2)) -> rcons(active(X1), X2) active(rcons(X1, X2)) -> rcons(X1, active(X2)) active(from(X)) -> from(active(X)) active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2) active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2)) active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2) active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2)) active(pi(X)) -> pi(active(X)) active(plus(X1, X2)) -> plus(active(X1), X2) active(plus(X1, X2)) -> plus(X1, active(X2)) active(times(X1, X2)) -> times(active(X1), X2) active(times(X1, X2)) -> times(X1, active(X2)) active(square(X)) -> square(active(X)) s(mark(X)) -> mark(s(X)) posrecip(mark(X)) -> mark(posrecip(X)) negrecip(mark(X)) -> mark(negrecip(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) rcons(mark(X1), X2) -> mark(rcons(X1, X2)) rcons(X1, mark(X2)) -> mark(rcons(X1, X2)) from(mark(X)) -> mark(from(X)) 2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2)) 2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2)) 2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2)) 2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2)) pi(mark(X)) -> mark(pi(X)) plus(mark(X1), X2) -> mark(plus(X1, X2)) plus(X1, mark(X2)) -> mark(plus(X1, X2)) times(mark(X1), X2) -> mark(times(X1, X2)) times(X1, mark(X2)) -> mark(times(X1, X2)) square(mark(X)) -> mark(square(X)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(posrecip(X)) -> posrecip(proper(X)) proper(negrecip(X)) -> negrecip(proper(X))
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