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TRS Standard pair #487069758
details
property
value
status
complete
benchmark
Ex7_BLR02_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n185.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.82177 seconds
cpu usage
3.92451
user time
3.73028
system time
0.19423
max virtual memory
1.8343376E7
max residence set size
246860.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 125 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: from(X) -> cons(X, n__from(s(X))) head(cons(X, XS)) -> X 2nd(cons(X, XS)) -> head(activate(XS)) take(0, XS) -> nil take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))) sel(0, cons(X, XS)) -> X sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) from(X) -> n__from(X) take(X1, X2) -> n__take(X1, X2) activate(n__from(X)) -> from(X) activate(n__take(X1, X2)) -> take(X1, X2) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: from/1(YES) cons/2(YES,YES) n__from/1)YES( s/1(YES) head/1(YES) 2nd/1(YES) activate/1(YES) take/2(YES,YES) 0/0) nil/0) n__take/2(YES,YES) sel/2(YES,YES) Quasi precedence: 2nd_1 > [from_1, activate_1, take_2] > s_1 > cons_2 > n__take_2 2nd_1 > [from_1, activate_1, take_2] > [0, nil] > n__take_2 2nd_1 > head_1 > n__take_2 sel_2 > [from_1, activate_1, take_2] > s_1 > cons_2 > n__take_2 sel_2 > [from_1, activate_1, take_2] > [0, nil] > n__take_2 Status: from_1: multiset status cons_2: multiset status s_1: multiset status head_1: multiset status 2nd_1: multiset status activate_1: multiset status take_2: multiset status 0: multiset status nil: multiset status n__take_2: multiset status sel_2: [1,2] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: from(X) -> cons(X, n__from(s(X))) head(cons(X, XS)) -> X 2nd(cons(X, XS)) -> head(activate(XS)) take(0, XS) -> nil take(s(N), cons(X, XS)) -> cons(X, n__take(N, activate(XS))) sel(0, cons(X, XS)) -> X sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) from(X) -> n__from(X) take(X1, X2) -> n__take(X1, X2) activate(n__take(X1, X2)) -> take(X1, X2) activate(X) -> X ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules:
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