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TRS Standard pair #516967685
details
property
value
status
complete
benchmark
#4.21.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n097.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.0286090374 seconds
cpu usage
5.246446468
max memory
4.72895488E8
stage attributes
key
value
output-size
1757
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES ----------------------------------------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(1) -> f(g(1)) f(f(x)) -> f(x) g(0) -> g(f(0)) g(g(x)) -> g(x) Q is empty. ---------------------------------------- (1) 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: f(1) -> f(g(1)) f(f(x)) -> f(x) g(0) -> g(f(0)) g(g(x)) -> g(x) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 3, 5, 6, 7, 8, 9, 10, 11, 12 Node 1 is start node and node 3 is final node. Those nodes are connected through the following edges: * 1 to 5 labelled f_1(0)* 1 to 3 labelled f_1(0), g_1(0), f_1(1), g_1(1)* 1 to 7 labelled g_1(0)* 1 to 9 labelled f_1(1)* 1 to 11 labelled g_1(1)* 3 to 3 labelled #_1(0)* 5 to 6 labelled g_1(0)* 6 to 3 labelled 1(0)* 7 to 8 labelled f_1(0)* 8 to 3 labelled 0(0)* 9 to 10 labelled g_1(1)* 10 to 3 labelled 1(1)* 11 to 12 labelled f_1(1)* 12 to 3 labelled 0(1) ---------------------------------------- (2) YES
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