details

property	value
status	complete
benchmark	Ex26_Luc03b_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n096.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.24971413612 seconds
cpu usage	13.17174959
max memory	1.223606272E9

stage attributes

key	value
output-size	21388
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 37 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 191 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 126 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 182 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N))) sqr(0) -> 0 sqr(s(X)) -> s(n__add(n__sqr(activate(X)), n__dbl(activate(X)))) dbl(0) -> 0 dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) add(0, X) -> X add(s(X), Y) -> s(n__add(activate(X), Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(activate(X), activate(Z))) terms(X) -> n__terms(X) s(X) -> n__s(X) add(X1, X2) -> n__add(X1, X2) sqr(X) -> n__sqr(X) dbl(X) -> n__dbl(X) first(X1, X2) -> n__first(X1, X2) activate(n__terms(X)) -> terms(activate(X)) activate(n__s(X)) -> s(X) activate(n__add(X1, X2)) -> add(activate(X1), activate(X2)) activate(n__sqr(X)) -> sqr(activate(X)) activate(n__dbl(X)) -> dbl(activate(X)) activate(n__first(X1, X2)) -> first(activate(X1), activate(X2)) activate(X) -> X Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: TERMS(N) -> SQR(N) SQR(s(X)) -> S(n__add(n__sqr(activate(X)), n__dbl(activate(X)))) SQR(s(X)) -> ACTIVATE(X) DBL(s(X)) -> S(n__s(n__dbl(activate(X)))) DBL(s(X)) -> ACTIVATE(X) ADD(s(X), Y) -> S(n__add(activate(X), Y)) ADD(s(X), Y) -> ACTIVATE(X) FIRST(s(X), cons(Y, Z)) -> ACTIVATE(X) FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z) ACTIVATE(n__terms(X)) -> TERMS(activate(X)) ACTIVATE(n__terms(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> S(X) ACTIVATE(n__add(X1, X2)) -> ADD(activate(X1), activate(X2)) ACTIVATE(n__add(X1, X2)) -> ACTIVATE(X1) ACTIVATE(n__add(X1, X2)) -> ACTIVATE(X2) ACTIVATE(n__sqr(X)) -> SQR(activate(X)) ACTIVATE(n__sqr(X)) -> ACTIVATE(X) ACTIVATE(n__dbl(X)) -> DBL(activate(X)) ACTIVATE(n__dbl(X)) -> ACTIVATE(X) ACTIVATE(n__first(X1, X2)) -> FIRST(activate(X1), activate(X2)) ACTIVATE(n__first(X1, X2)) -> ACTIVATE(X1) ACTIVATE(n__first(X1, X2)) -> ACTIVATE(X2) The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), n__terms(n__s(N))) sqr(0) -> 0 popout

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actions

all output return to TRS Stand 20472