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TRS Conte Sensi 17651 pair #381733279
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
n042.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.45537495613 seconds
cpu usage
3.410803377
max memory
2.05709312E8
stage attributes
key
value
output-size
11437
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSDependencyPairsProof [EQUIVALENT, 0 ms] (2) QCSDP (3) QCSDependencyGraphProof [EQUIVALENT, 0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
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