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TRS Standard pair #516962370
details
property
value
status
complete
benchmark
Ex1_2_Luc02c_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n002.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.08233809471 seconds
cpu usage
5.599336787
max memory
4.7020032E8
stage attributes
key
value
output-size
2295
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 102 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 2nd(cons(X, n__cons(Y, Z))) -> activate(Y) from(X) -> cons(X, n__from(n__s(X))) cons(X1, X2) -> n__cons(X1, X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [2nd_1, activate_1] > from_1 > cons_2 > n__cons_2 [2nd_1, activate_1] > from_1 > n__from_1 > n__cons_2 [2nd_1, activate_1] > from_1 > n__s_1 > n__cons_2 [2nd_1, activate_1] > s_1 > n__s_1 > n__cons_2 Status: 2nd_1: multiset status cons_2: multiset status n__cons_2: multiset status activate_1: multiset status from_1: multiset status n__from_1: multiset status n__s_1: multiset status s_1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 2nd(cons(X, n__cons(Y, Z))) -> activate(Y) from(X) -> cons(X, n__from(n__s(X))) cons(X1, X2) -> n__cons(X1, X2) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
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