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TRS Condi 20667 pair #381733015
details
property
value
status
complete
benchmark
quicksort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n100.star.cs.uiowa.edu
space
Mixed_CTRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.12343502045 seconds
cpu usage
5.076814055
max memory
2.83082752E8
stage attributes
key
value
output-size
20897
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 1 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) QDP (26) QReductionProof [EQUIVALENT, 1 ms] (27) QDP (28) QDPSizeChangeProof [EQUIVALENT, 0 ms] (29) YES (30) QDP (31) UsableRulesProof [EQUIVALENT, 0 ms] (32) QDP (33) QReductionProof [EQUIVALENT, 0 ms] (34) QDP (35) QDPOrderProof [EQUIVALENT, 33 ms] (36) QDP (37) PisEmptyProof [EQUIVALENT, 0 ms] (38) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: le(0, x) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, x) -> x app(cons(x, xs), ys) -> cons(x, app(xs, ys)) split(x, nil) -> pair(nil, nil) qsort(nil) -> nil The conditional TRS C consists of the following conditional rules: split(x, cons(y, ys)) -> pair(xs, cons(y, zs)) <= split(x, ys) -> pairs(xs, zs), le(x, y) -> true split(x, cons(y, ys)) -> pair(cons(y, xs), zs) <= split(x, ys) -> pairs(xs, zs), le(x, y) -> false qsort(cons(x, xs)) -> app(qsort(ys), cons(x, qsort(zs))) <= split(x, xs) -> pair(ys, zs) ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: split(x, cons(y, ys)) -> U1(split(x, ys), x, y) U1(pairs(xs, zs), x, y) -> U2(le(x, y), y, xs, zs) U2(false, y, xs, zs) -> pair(cons(y, xs), zs) U2(true, y, xs, zs) -> pair(xs, cons(y, zs)) qsort(cons(x, xs)) -> U3(split(x, xs), x) U3(pair(ys, zs), x) -> app(qsort(ys), cons(x, qsort(zs))) le(0, x) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, x) -> x app(cons(x, xs), ys) -> cons(x, app(xs, ys)) split(x, nil) -> pair(nil, nil) qsort(nil) -> nil
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