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TRS Contextsensitive pair #487092497
details
property
value
status
complete
benchmark
ExSec11_1_Luc02a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.6078 seconds
cpu usage
3.4664
user time
3.31859
system time
0.147811
max virtual memory
1.8408912E7
max residence set size
221236.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSDependencyPairsProof [EQUIVALENT, 16 ms] (2) QCSDP (3) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QCSDP (6) QCSDPSubtermProof [EQUIVALENT, 0 ms] (7) QCSDP (8) PIsEmptyProof [EQUIVALENT, 0 ms] (9) YES (10) QCSDP (11) QCSDPSubtermProof [EQUIVALENT, 0 ms] (12) QCSDP (13) PIsEmptyProof [EQUIVALENT, 0 ms] (14) YES (15) QCSDP (16) QCSDPSubtermProof [EQUIVALENT, 0 ms] (17) QCSDP (18) PIsEmptyProof [EQUIVALENT, 0 ms] (19) YES (20) QCSDP (21) QCSDPSubtermProof [EQUIVALENT, 0 ms] (22) QCSDP (23) PIsEmptyProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(add(sqr(X), dbl(X))) dbl(0) -> 0 dbl(s(X)) -> s(s(dbl(X))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) half(0) -> 0 half(s(0)) -> 0 half(s(s(X))) -> s(half(X)) half(dbl(X)) -> X The replacement map contains the following entries: terms: {1} cons: {1} recip: {1} sqr: {1} s: {1} 0: empty set add: {1, 2} dbl: {1} first: {1, 2} nil: empty set half: {1} ---------------------------------------- (1) CSDependencyPairsProof (EQUIVALENT) Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem. ---------------------------------------- (2) Obligation: Q-restricted context-sensitive dependency pair problem: The symbols in {terms_1, recip_1, sqr_1, s_1, add_2, dbl_1, first_2, half_1, SQR_1, TERMS_1, ADD_2, DBL_1, HALF_1} are replacing on all positions. For all symbols f in {cons_2} we have mu(f) = {1}. The ordinary context-sensitive dependency pairs DP_o are: TERMS(N) -> SQR(N) SQR(s(X)) -> ADD(sqr(X), dbl(X)) SQR(s(X)) -> SQR(X) SQR(s(X)) -> DBL(X) DBL(s(X)) -> DBL(X) ADD(s(X), Y) -> ADD(X, Y) HALF(s(s(X))) -> HALF(X) The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(add(sqr(X), dbl(X))) dbl(0) -> 0 dbl(s(X)) -> s(s(dbl(X))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) first(0, X) -> nil
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