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TRS Standard pair #516966905
details
property
value
status
complete
benchmark
2.48.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
SK90
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.23332691193 seconds
cpu usage
6.061616537
max memory
7.81774848E8
stage attributes
key
value
output-size
1798
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (2) YES ----------------------------------------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: d(x) -> e(u(x)) d(u(x)) -> c(x) c(u(x)) -> b(x) v(e(x)) -> x b(u(x)) -> a(e(x)) Q is empty. ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. The following rules were used to construct the certificate: d(x) -> e(u(x)) d(u(x)) -> c(x) c(u(x)) -> b(x) v(e(x)) -> x b(u(x)) -> a(e(x)) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 3, 4, 7, 8 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 3 labelled e_1(0)* 1 to 2 labelled c_1(0), b_1(0), d_1(0), e_1(0), u_1(0), v_1(0), a_1(0), b_1(1), c_1(1), d_1(1), e_1(1), u_1(1), v_1(1), a_1(1)* 1 to 1 labelled a_1(0), a_1(1)* 1 to 4 labelled e_1(1)* 1 to 7 labelled a_1(1)* 1 to 8 labelled e_1(2)* 2 to 2 labelled #_1(0)* 3 to 2 labelled u_1(0)* 4 to 2 labelled u_1(1)* 7 to 2 labelled e_1(1)* 8 to 2 labelled u_1(2) ---------------------------------------- (2) YES
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