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TRS Standard pair #487070628
details
property
value
status
complete
benchmark
Ex23_Luc06_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n189.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.69167 seconds
cpu usage
3.71681
user time
3.56385
system time
0.152958
max virtual memory
1.887486E7
max residence set size
268176.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(f(a)) -> c(n__f(n__g(n__f(n__a)))) f(X) -> n__f(X) g(X) -> n__g(X) a -> n__a activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(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 2. This implies Q-termination of R. The following rules were used to construct the certificate: f(f(a)) -> c(n__f(n__g(n__f(n__a)))) f(X) -> n__f(X) g(X) -> n__g(X) a -> n__a activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(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, 5, 6, 7, 8, 9, 15, 16, 17, 18, 19 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 5 labelled c_1(0)* 1 to 2 labelled n__f_1(0), n__g_1(0), n__a(0), a(0), f_1(0), c_1(0), g_1(0), activate_1(0), n__a(1), n__f_1(1), n__g_1(1), a(1), f_1(1), c_1(1), g_1(1), activate_1(1), n__a(2), n__f_1(2), n__g_1(2)* 1 to 9 labelled f_1(0), g_1(0), n__f_1(1), n__g_1(1), c_1(2)* 1 to 15 labelled c_1(1)* 1 to 19 labelled f_1(1), g_1(1), n__f_1(2), n__g_1(2)* 1 to 1 labelled f_1(1), g_1(1), n__f_1(2), n__g_1(2)* 2 to 2 labelled #_1(0)* 5 to 6 labelled n__f_1(0)* 6 to 7 labelled n__g_1(0)* 7 to 8 labelled n__f_1(0)* 8 to 2 labelled n__a(0)* 9 to 2 labelled activate_1(0), a(1), f_1(1), c_1(1), n__f_1(1), n__g_1(1), n__a(1), g_1(1), activate_1(1), n__a(2), n__f_1(2), n__g_1(2)* 9 to 1 labelled f_1(1), g_1(1), n__f_1(2), n__g_1(2)* 9 to 15 labelled c_1(1)* 9 to 9 labelled c_1(2)* 15 to 16 labelled n__f_1(1)* 16 to 17 labelled n__g_1(1)* 17 to 18 labelled n__f_1(1)* 18 to 2 labelled n__a(1)* 19 to 2 labelled activate_1(1), a(1), f_1(1), c_1(1), n__f_1(1), n__g_1(1), n__a(1), g_1(1), n__a(2), n__f_1(2), n__g_1(2)* 19 to 1 labelled f_1(1), g_1(1), n__f_1(2), n__g_1(2)* 19 to 15 labelled c_1(1)* 19 to 9 labelled c_1(2) ---------------------------------------- (2) YES
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