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TRS Standard pair #487069393
details
property
value
status
complete
benchmark
Ex1_Zan97_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n183.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.71964 seconds
cpu usage
3.80295
user time
3.62048
system time
0.18247
max virtual memory
1.8610432E7
max residence set size
234892.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES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: a__g(X) -> a__h(X) a__c -> d a__h(d) -> a__g(c) mark(g(X)) -> a__g(X) mark(h(X)) -> a__h(X) mark(c) -> a__c mark(d) -> d a__g(X) -> g(X) a__h(X) -> h(X) a__c -> c Q is empty. ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R. The following rules were used to construct the certificate: a__g(X) -> a__h(X) a__c -> d a__h(d) -> a__g(c) mark(g(X)) -> a__g(X) mark(h(X)) -> a__h(X) mark(c) -> a__c mark(d) -> d a__g(X) -> g(X) a__h(X) -> h(X) a__c -> c The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 3, 4 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 2 labelled a__h_1(0), d(0), a__g_1(0), a__c(0), g_1(0), h_1(0), c(0), h_1(1), a__h_1(1), g_1(1), d(1), c(1), h_1(2)* 1 to 3 labelled a__g_1(0), a__h_1(1), g_1(1), h_1(2)* 1 to 1 labelled a__g_1(1), a__h_1(2), g_1(2), h_1(3)* 1 to 4 labelled a__g_1(2), a__h_1(3), g_1(3), h_1(4)* 2 to 2 labelled #_1(0)* 3 to 2 labelled c(0)* 4 to 2 labelled c(2) ---------------------------------------- (2) YES
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