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TRS Condi 20667 pair #381733165
details
property
value
status
complete
benchmark
329.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n109.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.02785205841 seconds
cpu usage
4.687577709
max memory
2.34872832E8
stage attributes
key
value
output-size
20824
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 0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, 1 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, 0 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) QDP (26) QReductionProof [EQUIVALENT, 0 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, 28 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) -> pair(xs, zs), le(x, y) -> true split(x, cons(y, ys)) -> pair(cons(y, xs), zs) <= split(x, ys) -> pair(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(pair(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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