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Integer TRS Innermost pair #487528977
details
property
value
status
complete
benchmark
quicksort.itrs
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
Mixed_ITRS_2014
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.71541905403 seconds
cpu usage
6.859293791
max memory
4.8171008E8
stage attributes
key
value
output-size
88283
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.itrs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.itrs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ITRS could be proven: (0) ITRS (1) ITRStoIDPProof [EQUIVALENT, 0 ms] (2) IDP (3) ItpfGraphProof [EQUIVALENT, 11 ms] (4) IDP (5) IDependencyGraphProof [EQUIVALENT, 2 ms] (6) AND (7) IDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) IDP (10) IDPtoQDPProof [SOUND, 34 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) IDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) IDP (19) IDPNonInfProof [SOUND, 91 ms] (20) IDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES (23) IDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) IDP (26) IDPNonInfProof [SOUND, 241 ms] (27) IDP (28) IDependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE ---------------------------------------- (0) Obligation: ITRS problem: The following function symbols are pre-defined: <<< & ~ Bwand: (Integer, Integer) -> Integer >= ~ Ge: (Integer, Integer) -> Boolean | ~ Bwor: (Integer, Integer) -> Integer / ~ Div: (Integer, Integer) -> Integer != ~ Neq: (Integer, Integer) -> Boolean && ~ Land: (Boolean, Boolean) -> Boolean ! ~ Lnot: (Boolean) -> Boolean = ~ Eq: (Integer, Integer) -> Boolean <= ~ Le: (Integer, Integer) -> Boolean ^ ~ Bwxor: (Integer, Integer) -> Integer % ~ Mod: (Integer, Integer) -> Integer > ~ Gt: (Integer, Integer) -> Boolean + ~ Add: (Integer, Integer) -> Integer -1 ~ UnaryMinus: (Integer) -> Integer < ~ Lt: (Integer, Integer) -> Boolean || ~ Lor: (Boolean, Boolean) -> Boolean - ~ Sub: (Integer, Integer) -> Integer ~ ~ Bwnot: (Integer) -> Integer * ~ Mul: (Integer, Integer) -> Integer >>> The TRS R consists of the following rules: app(nil, zs) -> zs app(cons(x, ys), zs) -> cons(x, app(ys, zs)) split(x, e) -> pair(e, e) split(x, ins(y, zs)) -> Cond_split(x > y, x, ins(y, zs)) Cond_split(TRUE, x, ins(y, zs)) -> if_1(split(x, zs), x, y, zs) if_1(pair(zl, zh), x, y, zs) -> Cond_if_1(x > y, pair(zl, zh), x, y, zs) Cond_if_1(TRUE, pair(zl, zh), x, y, zs) -> pair(ins(y, zl), zh) split(x, ins(y, zs)) -> Cond_split1(y >= x, x, ins(y, zs)) Cond_split1(TRUE, x, ins(y, zs)) -> if_2(split(x, zs), x, y, zs) if_2(pair(zl, zh), x, y, zs) -> Cond_if_2(y >= x, pair(zl, zh), x, y, zs) Cond_if_2(TRUE, pair(zl, zh), x, y, zs) -> pair(zl, ins(y, zh)) qsort(e) -> nil qsort(ins(x, ys)) -> if_3(split(x, ys), x, ys) if_3(pair(yl, yh), x, ys) -> app(qsort(yl), cons(x, qsort(yh))) The set Q consists of the following terms: app(nil, x0) app(cons(x0, x1), x2) split(x0, e) split(x0, ins(x1, x2)) Cond_split(TRUE, x0, ins(x1, x2)) if_1(pair(x0, x1), x2, x3, x4) Cond_if_1(TRUE, pair(x0, x1), x2, x3, x4) Cond_split1(TRUE, x0, ins(x1, x2)) if_2(pair(x0, x1), x2, x3, x4) Cond_if_2(TRUE, pair(x0, x1), x2, x3, x4)
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