details

property	value
status	complete
benchmark	ExIntrod_GM01_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.24933004379 seconds
cpu usage	9.179961287
max memory	5.95910656E8

stage attributes

key	value
output-size	20463
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 101 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 7 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 18 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 21 ms] (8) QTRS (9) DependencyPairsProof [EQUIVALENT, 21 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) QDP (13) MRRProof [EQUIVALENT, 28 ms] (14) QDP (15) MRRProof [EQUIVALENT, 29 ms] (16) QDP (17) MRRProof [EQUIVALENT, 0 ms] (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 50 ms] (22) QDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__incr(nil) -> nil a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L)) a__adx(nil) -> nil a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L))) a__nats -> a__adx(a__zeros) a__zeros -> cons(0, zeros) a__head(cons(X, L)) -> mark(X) a__tail(cons(X, L)) -> mark(L) mark(incr(X)) -> a__incr(mark(X)) mark(adx(X)) -> a__adx(mark(X)) mark(nats) -> a__nats mark(zeros) -> a__zeros mark(head(X)) -> a__head(mark(X)) mark(tail(X)) -> a__tail(mark(X)) mark(nil) -> nil mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__incr(X) -> incr(X) a__adx(X) -> adx(X) a__nats -> nats a__zeros -> zeros a__head(X) -> head(X) a__tail(X) -> tail(X) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(a__adx(x_1)) = x_1 POL(a__head(x_1)) = 2*x_1 POL(a__incr(x_1)) = x_1 POL(a__nats) = 1 POL(a__tail(x_1)) = 2*x_1 POL(a__zeros) = 0 POL(adx(x_1)) = x_1 POL(cons(x_1, x_2)) = x_1 + x_2 POL(head(x_1)) = 2*x_1 POL(incr(x_1)) = x_1 POL(mark(x_1)) = x_1 POL(nats) = 1 POL(nil) = 0 POL(s(x_1)) = x_1 POL(tail(x_1)) = 2*x_1 POL(zeros) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__nats -> a__adx(a__zeros) popout

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actions

all output return to TRS Standard