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TRS Stand 20472 pair #381711471
details
property
value
status
complete
benchmark
nestrec.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n192.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.63361907005 seconds
cpu usage
3.781747439
max memory
2.83082752E8
stage attributes
key
value
output-size
2045
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0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: f(g(X)) -> g(f(f(X))) f(h(X)) -> h(g(X)) 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: g(f(X)) -> f(f(g(X))) h(f(X)) -> g(h(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: g(f(X)) -> f(f(g(X))) h(f(X)) -> g(h(X)) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 39, 40, 41, 42, 43, 44, 45, 46 Node 39 is start node and node 40 is final node. Those nodes are connected through the following edges: * 39 to 41 labelled f_1(0)* 39 to 43 labelled g_1(0)* 40 to 40 labelled #_1(0)* 41 to 42 labelled f_1(0)* 42 to 40 labelled g_1(0)* 42 to 44 labelled f_1(1)* 43 to 40 labelled h_1(0)* 43 to 46 labelled g_1(1)* 44 to 45 labelled f_1(1)* 45 to 40 labelled g_1(1)* 45 to 44 labelled f_1(1)* 46 to 40 labelled h_1(1)* 46 to 46 labelled g_1(1) ---------------------------------------- (4) YES
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