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TRS_Conditional 2019-03-28 22.59 pair #432272595
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
n098.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.85798 seconds
cpu usage
3.87725
user time
3.71456
system time
0.162694
max virtual memory
1.8408888E7
max residence set size
244572.0
stage attributes
key
value
starexec-result
YES
output
3.72/1.82 YES 3.83/1.83 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.83/1.83 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.83/1.83 3.83/1.83 3.83/1.83 Quasi decreasingness of the given CTRS could be proven: 3.83/1.83 3.83/1.83 (0) CTRS 3.83/1.83 (1) CTRSToQTRSProof [SOUND, 0 ms] 3.83/1.83 (2) QTRS 3.83/1.83 (3) QTRSRRRProof [EQUIVALENT, 109 ms] 3.83/1.83 (4) QTRS 3.83/1.83 (5) QTRSRRRProof [EQUIVALENT, 0 ms] 3.83/1.83 (6) QTRS 3.83/1.83 (7) RisEmptyProof [EQUIVALENT, 0 ms] 3.83/1.83 (8) YES 3.83/1.83 3.83/1.83 3.83/1.83 ---------------------------------------- 3.83/1.83 3.83/1.83 (0) 3.83/1.83 Obligation: 3.83/1.83 Conditional term rewrite system: 3.83/1.83 The TRS R consists of the following rules: 3.83/1.83 3.83/1.83 lte(0, n) -> true 3.83/1.83 lte(s(m), 0) -> false 3.83/1.83 lte(s(m), s(n)) -> lte(m, n) 3.83/1.83 insert(nil, m) -> cons(m, nil) 3.83/1.83 ordered(nil) -> true 3.83/1.83 ordered(cons(m, nil)) -> true 3.83/1.83 3.83/1.83 The conditional TRS C consists of the following conditional rules: 3.83/1.83 3.83/1.83 insert(cons(n, l), m) -> cons(m, cons(n, l)) <= lte(m, n) -> true 3.83/1.83 insert(cons(n, l), m) -> cons(n, insert(l, m)) <= lte(m, n) -> false 3.83/1.83 ordered(cons(m, cons(n, l))) -> ordered(cons(n, l)) <= lte(m, n) -> true 3.83/1.83 ordered(cons(m, cons(n, l))) -> false <= lte(m, n) -> false 3.83/1.83 3.83/1.83 3.83/1.83 ---------------------------------------- 3.83/1.83 3.83/1.83 (1) CTRSToQTRSProof (SOUND) 3.83/1.83 The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. 3.83/1.83 ---------------------------------------- 3.83/1.83 3.83/1.83 (2) 3.83/1.83 Obligation: 3.83/1.83 Q restricted rewrite system: 3.83/1.83 The TRS R consists of the following rules: 3.83/1.83 3.83/1.83 insert(cons(n, l), m) -> U1(lte(m, n), n, l, m) 3.83/1.83 U1(false, n, l, m) -> cons(n, insert(l, m)) 3.83/1.83 U1(true, n, l, m) -> cons(m, cons(n, l)) 3.83/1.83 ordered(cons(m, cons(n, l))) -> U2(lte(m, n), n, l) 3.83/1.83 U2(true, n, l) -> ordered(cons(n, l)) 3.83/1.83 U2(false, n, l) -> false 3.83/1.83 lte(0, n) -> true 3.83/1.83 lte(s(m), 0) -> false 3.83/1.83 lte(s(m), s(n)) -> lte(m, n) 3.83/1.83 insert(nil, m) -> cons(m, nil) 3.83/1.83 ordered(nil) -> true 3.83/1.83 ordered(cons(m, nil)) -> true 3.83/1.83 3.83/1.83 Q is empty. 3.83/1.83 3.83/1.83 ---------------------------------------- 3.83/1.83 3.83/1.83 (3) QTRSRRRProof (EQUIVALENT) 3.83/1.83 Used ordering: 3.83/1.83 insert/2(YES,YES) 3.83/1.83 cons/2(YES,YES) 3.83/1.83 U1/4(YES,YES,YES,YES) 3.83/1.83 lte/2(YES,YES) 3.83/1.83 false/0) 3.83/1.83 true/0) 3.83/1.83 ordered/1)YES( 3.83/1.83 U2/3(YES,YES,YES) 3.83/1.83 0/0) 3.83/1.83 s/1)YES( 3.83/1.83 nil/0) 3.83/1.83 3.83/1.83 Quasi precedence: 3.83/1.83 [insert_2, U1_4, nil] > [true, 0] > [cons_2, lte_2, U2_3] > false 3.83/1.83 3.83/1.83 3.83/1.83 Status: 3.83/1.83 insert_2: [1,2] 3.83/1.83 cons_2: [2,1] 3.83/1.83 U1_4: [3,4,1,2] 3.83/1.83 lte_2: [2,1] 3.83/1.83 false: multiset status 3.83/1.83 true: multiset status 3.83/1.83 U2_3: [3,2,1] 3.83/1.83 0: multiset status 3.83/1.83 nil: multiset status 3.83/1.83 3.83/1.83 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 3.83/1.83 3.83/1.83 insert(cons(n, l), m) -> U1(lte(m, n), n, l, m)
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