details

property	value
status	complete
benchmark	Ex18_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.59407 seconds
cpu usage	3.37183
user time	3.20169
system time	0.17014
max virtual memory	1.8808296E7
max residence set size	247828.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [SOUND, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(f(a)) -> a__f(g(f(a))) mark(f(X)) -> a__f(mark(X)) mark(a) -> a mark(g(X)) -> g(X) a__f(X) -> f(X) The set Q consists of the following terms: mark(f(x0)) mark(a) mark(g(x0)) a__f(x0) ---------------------------------------- (1) QTRS Reverse (SOUND) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a'(f(a__f(x))) -> a'(f(g(a__f(x)))) f(mark(X)) -> mark(a__f(X)) a'(mark(x)) -> a'(x) g(mark(X)) -> g(X) a__f(X) -> f(X) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. The following rules were used to construct the certificate: a'(f(a__f(x))) -> a'(f(g(a__f(x)))) f(mark(X)) -> mark(a__f(X)) a'(mark(x)) -> a'(x) g(mark(X)) -> g(X) a__f(X) -> f(X) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 3, 4, 5, 7, 9, 11, 12, 13 Node 3 is start node and node 4 is final node. Those nodes are connected through the following edges: * 3 to 5 labelled a'_1(0)* 3 to 9 labelled mark_1(0)* 3 to 4 labelled a'_1(0), g_1(0), f_1(0), a'_1(1), g_1(1)* 3 to 11 labelled a'_1(1)* 3 to 13 labelled mark_1(1)* 4 to 4 labelled #_1(0)* 5 to 7 labelled f_1(0)* 7 to 9 labelled g_1(0)* 7 to 13 labelled g_1(1), g_1(2)* 9 to 4 labelled a__f_1(0), f_1(1)* 9 to 13 labelled mark_1(1)* 11 to 12 labelled f_1(1)* 12 to 13 labelled g_1(1), g_1(2)* 13 to 4 labelled a__f_1(1), f_1(2)* 13 to 13 labelled mark_1(1) ---------------------------------------- (4) YES popout

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job log

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actions

all output return to TRS Innermost