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TRS Standard pair #487070713
details
property
value
status
complete
benchmark
Ex18_Luc06_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.73564 seconds
cpu usage
3.56328
user time
3.39372
system time
0.169559
max virtual memory
1.8411536E7
max residence set size
257328.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(f(a)) -> f(g(n__f(n__a))) f(X) -> n__f(X) a -> n__a activate(n__f(X)) -> f(activate(X)) activate(n__a) -> a activate(X) -> X Q is empty. ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. This implies Q-termination of R. The following rules were used to construct the certificate: f(f(a)) -> f(g(n__f(n__a))) f(X) -> n__f(X) a -> n__a activate(n__f(X)) -> f(activate(X)) activate(n__a) -> a activate(X) -> X The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 3 labelled f_1(0), n__f_1(1)* 1 to 2 labelled n__f_1(0), n__a(0), a(0), f_1(0), g_1(0), activate_1(0), n__a(1), n__f_1(1), a(1), f_1(1), g_1(1), activate_1(1), n__a(2), n__f_1(2)* 1 to 6 labelled f_1(1), n__f_1(2)* 1 to 1 labelled f_1(1), n__f_1(2)* 1 to 9 labelled f_1(2), n__f_1(3)* 2 to 2 labelled #_1(0)* 3 to 4 labelled g_1(0)* 3 to 2 labelled activate_1(0), a(1), f_1(1), g_1(1), n__f_1(1), n__a(1), activate_1(1), n__a(2), n__f_1(2)* 3 to 1 labelled f_1(1), n__f_1(2)* 3 to 6 labelled f_1(1), n__f_1(2)* 3 to 9 labelled f_1(2), n__f_1(3)* 4 to 5 labelled n__f_1(0)* 5 to 2 labelled n__a(0)* 6 to 7 labelled g_1(1)* 6 to 2 labelled activate_1(1), a(1), f_1(1), g_1(1), n__f_1(1), n__a(1), n__a(2), n__f_1(2)* 6 to 1 labelled f_1(1), n__f_1(2)* 6 to 6 labelled f_1(1), n__f_1(2)* 6 to 9 labelled f_1(2), n__f_1(3)* 7 to 8 labelled n__f_1(1)* 8 to 2 labelled n__a(1)* 9 to 10 labelled g_1(2)* 10 to 11 labelled n__f_1(2)* 11 to 2 labelled n__a(2) ---------------------------------------- (2) YES
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