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TRS Conditional pair #487562856
details
property
value
status
complete
benchmark
272.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.96928191185 seconds
cpu usage
4.171727056
max memory
2.48557568E8
stage attributes
key
value
output-size
3914
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 130 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: lte(0, n) -> true lte(s(m), 0) -> false lte(s(m), s(n)) -> lte(m, n) insert(nil, m) -> cons(m, nil) ordered(nil) -> true ordered(cons(m, nil)) -> true The conditional TRS C consists of the following conditional rules: insert(cons(n, l), m) -> cons(m, cons(n, l)) <= lte(m, n) -> true insert(cons(n, l), m) -> cons(n, insert(l, m)) <= lte(m, n) -> false ordered(cons(m, cons(n, l))) -> ordered(cons(n, l)) <= lte(m, n) -> true ordered(cons(m, cons(n, l))) -> false <= lte(m, n) -> false ---------------------------------------- (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: insert(cons(n, l), m) -> U1(lte(m, n), n, l, m) U1(false, n, l, m) -> cons(n, insert(l, m)) U1(true, n, l, m) -> cons(m, cons(n, l)) ordered(cons(m, cons(n, l))) -> U2(lte(m, n), n, l) U2(true, n, l) -> ordered(cons(n, l)) U2(false, n, l) -> false lte(0, n) -> true lte(s(m), 0) -> false lte(s(m), s(n)) -> lte(m, n) insert(nil, m) -> cons(m, nil) ordered(nil) -> true ordered(cons(m, nil)) -> true Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: insert/2(YES,YES) cons/2(YES,YES) U1/4(YES,YES,YES,YES) lte/2(YES,YES) false/0) true/0) ordered/1)YES( U2/3(YES,YES,YES) 0/0) s/1)YES( nil/0) Quasi precedence: [insert_2, U1_4, nil] > [true, 0] > [cons_2, lte_2, U2_3] > false Status: insert_2: [1,2] cons_2: [2,1] U1_4: [3,4,1,2] lte_2: [2,1] false: multiset status true: multiset status U2_3: [3,2,1]
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