details

property	value
status	complete
benchmark	Ex14_Luc06_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.07197 seconds
cpu usage	4.74336
user time	4.48805
system time	0.255317
max virtual memory	1.8543288E7
max residence set size	341072.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 52 ms] (4) CSR (5) CSDependencyPairsProof [EQUIVALENT, 0 ms] (6) QCSDP (7) QCSDPInstantiationProcessor [EQUIVALENT, 0 ms] (8) QCSDP (9) QCSUsableRulesProof [EQUIVALENT, 0 ms] (10) QCSDP (11) QCSDPInstantiationProcessor [EQUIVALENT, 0 ms] (12) QCSDP (13) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(h(X)) -> mark(g(X, X)) active(g(a, X)) -> mark(f(b, X)) active(f(X, X)) -> mark(h(a)) active(a) -> mark(b) active(h(X)) -> h(active(X)) active(g(X1, X2)) -> g(active(X1), X2) active(f(X1, X2)) -> f(active(X1), X2) h(mark(X)) -> mark(h(X)) g(mark(X1), X2) -> mark(g(X1, X2)) f(mark(X1), X2) -> mark(f(X1, X2)) proper(h(X)) -> h(proper(X)) proper(g(X1, X2)) -> g(proper(X1), proper(X2)) proper(a) -> ok(a) proper(f(X1, X2)) -> f(proper(X1), proper(X2)) proper(b) -> ok(b) h(ok(X)) -> ok(h(X)) g(ok(X1), ok(X2)) -> ok(g(X1, X2)) f(ok(X1), ok(X2)) -> ok(f(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. ---------------------------------------- (1) QTRSToCSRProof (EQUIVALENT) The following Q TRS is given: Q restricted rewrite system: The TRS R consists of the following rules: active(h(X)) -> mark(g(X, X)) active(g(a, X)) -> mark(f(b, X)) active(f(X, X)) -> mark(h(a)) active(a) -> mark(b) active(h(X)) -> h(active(X)) active(g(X1, X2)) -> g(active(X1), X2) active(f(X1, X2)) -> f(active(X1), X2) h(mark(X)) -> mark(h(X)) g(mark(X1), X2) -> mark(g(X1, X2)) f(mark(X1), X2) -> mark(f(X1, X2)) proper(h(X)) -> h(proper(X)) proper(g(X1, X2)) -> g(proper(X1), proper(X2)) proper(a) -> ok(a) proper(f(X1, X2)) -> f(proper(X1), proper(X2)) proper(b) -> ok(b) h(ok(X)) -> ok(h(X)) g(ok(X1), ok(X2)) -> ok(g(X1, X2)) f(ok(X1), ok(X2)) -> ok(f(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. Special symbols used for the transformation (see [GM04]): top: top_1, active: active_1, mark: mark_1, ok: ok_1, proper: proper_1 The replacement map contains the following entries: h: {1} g: {1} a: empty set f: {1} b: empty set The QTRS contained all rules created by the complete Giesl-Middeldorp transformation. Therefore, the inverse transformation is complete (and sound). ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: h(X) -> g(X, X) popout

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job log

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actions

all output return to TRS Standard