details

property	value
status	complete
benchmark	Ex26_Luc03b_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.89167 seconds
cpu usage	8.0123
user time	7.66224
system time	0.350057
max virtual memory	1.8490208E7
max residence set size	573484.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 16 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 134 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 87 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(n__add(sqr(activate(X)), 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) add(X1, X2) -> n__add(X1, X2) s(X) -> n__s(X) dbl(X) -> n__dbl(X) first(X1, X2) -> n__first(X1, X2) activate(n__terms(X)) -> terms(X) activate(n__add(X1, X2)) -> add(X1, X2) activate(n__s(X)) -> s(X) activate(n__dbl(X)) -> dbl(X) activate(n__first(X1, X2)) -> first(X1, 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) TERMS(N) -> S(N) SQR(s(X)) -> S(n__add(sqr(activate(X)), dbl(activate(X)))) SQR(s(X)) -> SQR(activate(X)) SQR(s(X)) -> ACTIVATE(X) SQR(s(X)) -> DBL(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(X) ACTIVATE(n__add(X1, X2)) -> ADD(X1, X2) ACTIVATE(n__s(X)) -> S(X) ACTIVATE(n__dbl(X)) -> DBL(X) ACTIVATE(n__first(X1, X2)) -> FIRST(X1, X2) The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(n__add(sqr(activate(X)), 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) add(X1, X2) -> n__add(X1, X2) s(X) -> n__s(X) dbl(X) -> n__dbl(X) first(X1, X2) -> n__first(X1, X2) activate(n__terms(X)) -> terms(X) activate(n__add(X1, X2)) -> add(X1, X2) activate(n__s(X)) -> s(X) popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard