details

property	value
status	complete
benchmark	Ex14_AEGL02_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.75074 seconds
cpu usage	3.75003
user time	3.58658
system time	0.163448
max virtual memory	1.840914E7
max residence set size	241132.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 56 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 0 ms] (8) CSR (9) RisEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(from(X)) -> mark(cons(X, from(s(X)))) active(length(nil)) -> mark(0) active(length(cons(X, Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) active(from(X)) -> from(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(s(X)) -> s(active(X)) from(mark(X)) -> mark(from(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) s(mark(X)) -> mark(s(X)) proper(from(X)) -> from(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(length(X)) -> length(proper(X)) proper(nil) -> ok(nil) proper(0) -> ok(0) proper(length1(X)) -> length1(proper(X)) from(ok(X)) -> ok(from(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) s(ok(X)) -> ok(s(X)) length(ok(X)) -> ok(length(X)) length1(ok(X)) -> ok(length1(X)) 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(from(X)) -> mark(cons(X, from(s(X)))) active(length(nil)) -> mark(0) active(length(cons(X, Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) active(from(X)) -> from(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(s(X)) -> s(active(X)) from(mark(X)) -> mark(from(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) s(mark(X)) -> mark(s(X)) proper(from(X)) -> from(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(length(X)) -> length(proper(X)) proper(nil) -> ok(nil) proper(0) -> ok(0) proper(length1(X)) -> length1(proper(X)) from(ok(X)) -> ok(from(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) s(ok(X)) -> ok(s(X)) length(ok(X)) -> ok(length(X)) length1(ok(X)) -> ok(length1(X)) 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: from: {1} cons: {1} s: {1} length: empty set nil: empty set 0: empty set length1: empty set The QTRS contained all rules created by the complete Giesl-Middeldorp transformation. Therefore, the inverse transformation is complete (and sound). ---------------------------------------- popout

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actions

all output return to TRS Standard