details

property	value
status	complete
benchmark	#3.51.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.5469 seconds
cpu usage	3.39248
user time	3.24013
system time	0.152351
max virtual memory	1.8543636E7
max residence set size	238616.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0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(x)) -> f(c(f(x))) f(f(x)) -> f(d(f(x))) g(c(x)) -> x g(d(x)) -> x g(c(h(0))) -> g(d(1)) g(c(1)) -> g(d(h(0))) g(h(x)) -> g(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: f(f(x)) -> f(c(f(x))) f(f(x)) -> f(d(f(x))) c(g(x)) -> x d(g(x)) -> x 0'(h(c(g(x)))) -> 1'(d(g(x))) 1'(c(g(x))) -> 0'(h(d(g(x)))) h(g(x)) -> g(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: f(f(x)) -> f(c(f(x))) f(f(x)) -> f(d(f(x))) c(g(x)) -> x d(g(x)) -> x 0'(h(c(g(x)))) -> 1'(d(g(x))) 1'(c(g(x))) -> 0'(h(d(g(x)))) h(g(x)) -> g(x) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 3, 4, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 Node 3 is start node and node 4 is final node. Those nodes are connected through the following edges: * 3 to 23 labelled f_1(0)* 3 to 25 labelled f_1(0)* 3 to 4 labelled f_1(0), c_1(0), d_1(0), g_1(0), 0'_1(0), h_1(0), 1'_1(0), f_1(1), c_1(1), d_1(1), g_1(1), 0'_1(1), h_1(1), 1'_1(1)* 3 to 27 labelled 1'_1(0)* 3 to 29 labelled 0'_1(0)* 3 to 32 labelled f_1(1)* 3 to 34 labelled f_1(1)* 3 to 36 labelled 1'_1(1)* 3 to 38 labelled 0'_1(1)* 4 to 4 labelled #_1(0)* 23 to 24 labelled c_1(0)* 24 to 4 labelled f_1(0)* 24 to 32 labelled f_1(1)* 24 to 34 labelled f_1(1)* 25 to 26 labelled d_1(0)* 26 to 4 labelled f_1(0)* 26 to 32 labelled f_1(1)* 26 to 34 labelled f_1(1)* 27 to 28 labelled d_1(0)* 27 to 4 labelled f_1(1), c_1(1), d_1(1), g_1(1), 0'_1(1), h_1(1), 1'_1(1)* 27 to 32 labelled f_1(1)* 27 to 34 labelled f_1(1)* 27 to 36 labelled 1'_1(1)* 27 to 38 labelled 0'_1(1)* 28 to 4 labelled g_1(0)* 29 to 30 labelled h_1(0)* 29 to 4 labelled g_1(1)* 30 to 31 labelled d_1(0)* 30 to 4 labelled f_1(1), c_1(1), d_1(1), g_1(1), 0'_1(1), h_1(1), 1'_1(1)* 30 to 32 labelled f_1(1)* 30 to 34 labelled f_1(1)* 30 to 36 labelled 1'_1(1)* 30 to 38 labelled 0'_1(1)* 31 to 4 labelled g_1(0)* 32 to 33 labelled c_1(1)* 33 to 4 labelled f_1(1)* 33 to 32 labelled f_1(1)* 33 to 34 labelled f_1(1)* 34 to 35 labelled d_1(1)* 35 to 4 labelled f_1(1)* 35 to 32 labelled f_1(1)* 35 to 34 labelled f_1(1)* 36 to 37 labelled d_1(1)* 36 to 4 labelled f_1(1), c_1(1), d_1(1), g_1(1), 0'_1(1), h_1(1), 1'_1(1)* 36 to 32 labelled f_1(1)* 36 to 34 labelled f_1(1)* 36 to 36 labelled 1'_1(1)* 36 to 38 labelled 0'_1(1)* 37 to 4 labelled g_1(1)* 38 to 39 labelled h_1(1)* 38 to 4 labelled g_1(2)* 39 to 40 labelled d_1(1)* 39 to 4 labelled f_1(1), c_1(1), d_1(1), g_1(1), 0'_1(1), h_1(1), 1'_1(1)* 39 to 32 labelled f_1(1)* 39 to 34 labelled f_1(1)* 39 to 36 labelled 1'_1(1)* 39 to 38 labelled 0'_1(1)* 40 to 4 labelled g_1(1) ---------------------------------------- (4) YES popout

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

job log

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actions

all output return to TRS Standard