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TRS Stand 20472 pair #381710297
details
property
value
status
complete
benchmark
qsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n089.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
12.0122990608 seconds
cpu usage
32.610769802
max memory
2.42079744E9
stage attributes
key
value
output-size
72484
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 19 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) QDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) QDP (24) QReductionProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES (28) QDP (29) UsableRulesProof [EQUIVALENT, 0 ms] (30) QDP (31) QReductionProof [EQUIVALENT, 0 ms] (32) QDP (33) QDPSizeChangeProof [EQUIVALENT, 0 ms] (34) YES (35) QDP (36) UsableRulesProof [EQUIVALENT, 0 ms] (37) QDP (38) QReductionProof [EQUIVALENT, 0 ms] (39) QDP (40) TransformationProof [EQUIVALENT, 3 ms] (41) QDP (42) TransformationProof [EQUIVALENT, 0 ms] (43) QDP (44) Induction-Processor [SOUND, 15 ms] (45) AND (46) QDP (47) UsableRulesProof [EQUIVALENT, 0 ms] (48) QDP (49) QReductionProof [EQUIVALENT, 0 ms] (50) QDP (51) Induction-Processor [SOUND, 5 ms] (52) AND (53) QDP (54) PisEmptyProof [EQUIVALENT, 0 ms] (55) YES (56) QTRS (57) QTRSRRRProof [EQUIVALENT, 54 ms] (58) QTRS (59) QTRSRRRProof [EQUIVALENT, 0 ms] (60) QTRS (61) RisEmptyProof [EQUIVALENT, 0 ms] (62) YES (63) QTRS (64) QTRSRRRProof [EQUIVALENT, 68 ms] (65) QTRS (66) QTRSRRRProof [EQUIVALENT, 0 ms] (67) QTRS (68) RisEmptyProof [EQUIVALENT, 0 ms] (69) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: qsort(nil) -> nil qsort(cons(x, xs)) -> append(qsort(filterlow(x, cons(x, xs))), cons(x, qsort(filterhigh(x, cons(x, xs))))) filterlow(n, nil) -> nil filterlow(n, cons(x, xs)) -> if1(ge(n, x), n, x, xs) if1(true, n, x, xs) -> filterlow(n, xs) if1(false, n, x, xs) -> cons(x, filterlow(n, xs)) filterhigh(n, nil) -> nil filterhigh(n, cons(x, xs)) -> if2(ge(x, n), n, x, xs)
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