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TRS Standard pair #516964185
details
property
value
status
complete
benchmark
06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n029.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.24227905273 seconds
cpu usage
5.872850662
max memory
5.35990272E8
stage attributes
key
value
output-size
1540
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 4 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(g(x)) -> g(g(f(x))) f(g(x)) -> g(g(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(g(x)) -> g(g(f(x))) f(g(x)) -> g(g(g(x))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 3, 4, 5, 6 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 3 labelled g_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled g_1(0)* 4 to 2 labelled f_1(0), g_1(0)* 4 to 5 labelled g_1(1)* 5 to 6 labelled g_1(1)* 6 to 2 labelled f_1(1), g_1(1)* 6 to 5 labelled g_1(1) ---------------------------------------- (2) YES
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