details

property	value
status	complete
benchmark	Ex18_Luc06_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.54296 seconds
cpu usage	3.38062
user time	3.21854
system time	0.162079
max virtual memory	1.8478328E7
max residence set size	235604.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0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: f(f(a)) -> f(g(n__f(a))) f(X) -> n__f(X) activate(n__f(X)) -> f(X) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a'(f(f(x))) -> a'(n__f(g(f(x)))) f(X) -> n__f(X) n__f(activate(X)) -> f(X) activate(X) -> 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(f(x))) -> a'(n__f(g(f(x)))) f(X) -> n__f(X) n__f(activate(X)) -> f(X) activate(X) -> X The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 2, 10, 11, 12, 13, 14, 15, 16 Node 2 is start node and node 10 is final node. Those nodes are connected through the following edges: * 2 to 11 labelled a'_1(0)* 2 to 10 labelled n__f_1(0), f_1(0), a'_1(0), g_1(0), activate_1(0), n__f_1(1), f_1(1), a'_1(1), g_1(1), activate_1(1), n__f_1(2)* 2 to 14 labelled a'_1(1)* 10 to 10 labelled #_1(0)* 11 to 12 labelled n__f_1(0)* 12 to 13 labelled g_1(0)* 13 to 10 labelled f_1(0), n__f_1(1), f_1(1), n__f_1(2)* 14 to 15 labelled n__f_1(1)* 15 to 16 labelled g_1(1)* 16 to 10 labelled f_1(1), n__f_1(2) ---------------------------------------- (4) YES popout

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

job log

popout

actions

all output return to TRS Standard