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TRS_Innermost 2019-03-28 22.12 pair #432270898
details
property
value
status
complete
benchmark
Ex3_3_25_Bor03_L.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n129.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.62021 seconds
cpu usage
3.53938
user time
3.36533
system time
0.17405
max virtual memory
1.8277584E7
max residence set size
227604.0
stage attributes
key
value
starexec-result
YES
output
3.31/1.58 YES 3.31/1.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.31/1.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.31/1.59 3.31/1.59 3.31/1.59 Termination w.r.t. Q of the given QTRS could be proven: 3.31/1.59 3.31/1.59 (0) QTRS 3.31/1.59 (1) QTRSRRRProof [EQUIVALENT, 27 ms] 3.31/1.59 (2) QTRS 3.31/1.59 (3) RisEmptyProof [EQUIVALENT, 0 ms] 3.31/1.59 (4) YES 3.31/1.59 3.31/1.59 3.31/1.59 ---------------------------------------- 3.31/1.59 3.31/1.59 (0) 3.31/1.59 Obligation: 3.31/1.59 Q restricted rewrite system: 3.31/1.59 The TRS R consists of the following rules: 3.31/1.59 3.31/1.59 app(nil, YS) -> YS 3.31/1.59 app(cons(X), YS) -> cons(X) 3.31/1.59 from(X) -> cons(X) 3.31/1.59 zWadr(nil, YS) -> nil 3.31/1.59 zWadr(XS, nil) -> nil 3.31/1.59 zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X))) 3.31/1.59 prefix(L) -> cons(nil) 3.31/1.59 3.31/1.59 The set Q consists of the following terms: 3.31/1.59 3.31/1.59 app(nil, x0) 3.31/1.59 app(cons(x0), x1) 3.31/1.59 from(x0) 3.31/1.59 zWadr(nil, x0) 3.31/1.59 zWadr(x0, nil) 3.31/1.59 zWadr(cons(x0), cons(x1)) 3.31/1.59 prefix(x0) 3.31/1.59 3.31/1.59 3.31/1.59 ---------------------------------------- 3.31/1.59 3.31/1.59 (1) QTRSRRRProof (EQUIVALENT) 3.31/1.59 Used ordering: 3.31/1.59 Knuth-Bendix order [KBO] with precedence:nil > zWadr_2 > from_1 > prefix_1 > cons_1 > app_2 3.31/1.59 3.31/1.59 and weight map: 3.31/1.59 3.31/1.59 nil=2 3.31/1.59 cons_1=1 3.31/1.59 from_1=1 3.31/1.59 prefix_1=2 3.31/1.59 app_2=0 3.31/1.59 zWadr_2=0 3.31/1.59 3.31/1.59 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 3.31/1.59 3.31/1.59 app(nil, YS) -> YS 3.31/1.59 app(cons(X), YS) -> cons(X) 3.31/1.59 from(X) -> cons(X) 3.31/1.59 zWadr(nil, YS) -> nil 3.31/1.59 zWadr(XS, nil) -> nil 3.31/1.59 zWadr(cons(X), cons(Y)) -> cons(app(Y, cons(X))) 3.31/1.59 prefix(L) -> cons(nil) 3.31/1.59 3.31/1.59 3.31/1.59 3.31/1.59 3.31/1.59 ---------------------------------------- 3.31/1.59 3.31/1.59 (2) 3.31/1.59 Obligation: 3.31/1.59 Q restricted rewrite system: 3.31/1.59 R is empty. 3.31/1.59 The set Q consists of the following terms: 3.31/1.59 3.31/1.59 app(nil, x0) 3.31/1.59 app(cons(x0), x1) 3.31/1.59 from(x0) 3.31/1.59 zWadr(nil, x0) 3.31/1.59 zWadr(x0, nil) 3.31/1.59 zWadr(cons(x0), cons(x1)) 3.31/1.59 prefix(x0) 3.31/1.59 3.31/1.59 3.31/1.59 ---------------------------------------- 3.31/1.59 3.31/1.59 (3) RisEmptyProof (EQUIVALENT) 3.31/1.59 The TRS R is empty. Hence, termination is trivially proven. 3.31/1.59 ---------------------------------------- 3.31/1.59 3.31/1.59 (4) 3.31/1.59 YES 3.31/1.62 EOF
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