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TRS Stand 20472 pair #381710631
details
property
value
status
complete
benchmark
ex5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n095.star.cs.uiowa.edu
space
AProVE_10
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.52583503723 seconds
cpu usage
3.356870429
max memory
2.28253696E8
stage attributes
key
value
output-size
1823
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0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: g(0) -> 0 g(s(x)) -> f(g(x)) f(0) -> 0 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: 0'(g(x)) -> 0'(x) s(g(x)) -> g(f(x)) 0'(f(x)) -> 0'(x) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. The following rules were used to construct the certificate: 0'(g(x)) -> 0'(x) s(g(x)) -> g(f(x)) 0'(f(x)) -> 0'(x) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 2, 4, 6 Node 2 is start node and node 4 is final node. Those nodes are connected through the following edges: * 2 to 4 labelled 0'_1(0), 0'_1(1)* 2 to 6 labelled g_1(0)* 4 to 4 labelled #_1(0)* 6 to 4 labelled f_1(0) ---------------------------------------- (4) YES
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