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TRS Stand 20472 pair #381715867
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
n025.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.52074790001 seconds
cpu usage
3.356504253
max memory
2.35626496E8
stage attributes
key
value
output-size
1971
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES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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