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	n075.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.6418 seconds
cpu usage	3.47256
user time	3.31467
system time	0.157888
max virtual memory	1.8409116E7
max residence set size	232004.0

stage attributes

key	value
starexec-result	YES

output

3.32/1.59 YES 3.32/1.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.32/1.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.32/1.60 3.32/1.60 3.32/1.60 Termination of the given CSR could be proven: 3.32/1.60 3.32/1.60 (0) CSR 3.32/1.60 (1) CSDependencyPairsProof [EQUIVALENT, 0 ms] 3.32/1.60 (2) QCSDP 3.32/1.60 (3) QCSDependencyGraphProof [EQUIVALENT, 0 ms] 3.32/1.60 (4) AND 3.32/1.60 (5) QCSDP 3.32/1.60 (6) QCSDPSubtermProof [EQUIVALENT, 0 ms] 3.32/1.60 (7) QCSDP 3.32/1.60 (8) PIsEmptyProof [EQUIVALENT, 0 ms] 3.32/1.60 (9) YES 3.32/1.60 (10) QCSDP 3.32/1.60 (11) QCSDPSubtermProof [EQUIVALENT, 0 ms] 3.32/1.60 (12) QCSDP 3.32/1.60 (13) PIsEmptyProof [EQUIVALENT, 0 ms] 3.32/1.60 (14) YES 3.32/1.60 (15) QCSDP 3.32/1.60 (16) QCSDPSubtermProof [EQUIVALENT, 0 ms] 3.32/1.60 (17) QCSDP 3.32/1.60 (18) PIsEmptyProof [EQUIVALENT, 0 ms] 3.32/1.60 (19) YES 3.32/1.60 (20) QCSDP 3.32/1.60 (21) QCSDPSubtermProof [EQUIVALENT, 0 ms] 3.32/1.60 (22) QCSDP 3.32/1.60 (23) PIsEmptyProof [EQUIVALENT, 0 ms] 3.32/1.60 (24) YES 3.32/1.60 3.32/1.60 3.32/1.60 ---------------------------------------- 3.32/1.60 3.32/1.60 (0) 3.32/1.60 Obligation: 3.32/1.60 Context-sensitive rewrite system: 3.32/1.60 The TRS R consists of the following rules: 3.32/1.60 3.32/1.60 terms(N) -> cons(recip(sqr(N)), terms(s(N))) 3.32/1.60 sqr(0) -> 0 3.32/1.60 sqr(s(X)) -> s(add(sqr(X), dbl(X))) 3.32/1.60 dbl(0) -> 0 3.32/1.60 dbl(s(X)) -> s(s(dbl(X))) 3.32/1.60 add(0, X) -> X 3.32/1.60 add(s(X), Y) -> s(add(X, Y)) 3.32/1.60 first(0, X) -> nil 3.32/1.60 first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) 3.32/1.60 half(0) -> 0 3.32/1.60 half(s(0)) -> 0 3.32/1.60 half(s(s(X))) -> s(half(X)) 3.32/1.60 half(dbl(X)) -> X 3.32/1.60 3.32/1.60 The replacement map contains the following entries: 3.32/1.60 3.32/1.60 terms: {1} 3.32/1.60 cons: {1} 3.32/1.60 recip: {1} 3.32/1.60 sqr: {1} 3.32/1.60 s: {1} 3.32/1.60 0: empty set 3.32/1.60 add: {1, 2} 3.32/1.60 dbl: {1} 3.32/1.60 first: {1, 2} 3.32/1.60 nil: empty set 3.32/1.60 half: {1} 3.32/1.60 3.32/1.60 ---------------------------------------- 3.32/1.60 3.32/1.60 (1) CSDependencyPairsProof (EQUIVALENT) 3.32/1.60 Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem. 3.32/1.60 ---------------------------------------- 3.32/1.60 3.32/1.60 (2) 3.32/1.60 Obligation: 3.32/1.60 Q-restricted context-sensitive dependency pair problem: 3.32/1.60 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. 3.32/1.60 For all symbols f in {cons_2} we have mu(f) = {1}. 3.32/1.60 3.32/1.60 The ordinary context-sensitive dependency pairs DP_o are: 3.32/1.60 TERMS(N) -> SQR(N) 3.32/1.60 SQR(s(X)) -> ADD(sqr(X), dbl(X)) 3.32/1.60 SQR(s(X)) -> SQR(X) 3.32/1.60 SQR(s(X)) -> DBL(X) 3.32/1.60 DBL(s(X)) -> DBL(X) 3.32/1.60 ADD(s(X), Y) -> ADD(X, Y) 3.32/1.60 HALF(s(s(X))) -> HALF(X) 3.32/1.60 3.32/1.60 The TRS R consists of the following rules: 3.32/1.60 3.32/1.60 terms(N) -> cons(recip(sqr(N)), terms(s(N))) 3.32/1.60 sqr(0) -> 0 3.32/1.60 sqr(s(X)) -> s(add(sqr(X), dbl(X))) 3.32/1.60 dbl(0) -> 0 3.32/1.60 dbl(s(X)) -> s(s(dbl(X))) 3.32/1.60 add(0, X) -> X 3.32/1.60 add(s(X), Y) -> s(add(X, Y)) 3.32/1.60 first(0, X) -> nil popout

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job log

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actions

all output return to TRS_Contextsensitive 2019-03-21 05.07