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TRS Standard pair #487071043
details
property
value
status
complete
benchmark
Ex4_Zan97_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n187.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.64782 seconds
cpu usage
3.84344
user time
3.68658
system time
0.156862
max virtual memory
1.8343148E7
max residence set size
233492.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 34 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(X) -> cons(X, n__f(n__g(X))) g(0) -> s(0) g(s(X)) -> s(s(g(X))) sel(0, cons(X, Y)) -> X sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) f(X) -> n__f(X) g(X) -> n__g(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: sel_2 > activate_1 > f_1 > cons_2 > n__f_1 sel_2 > activate_1 > f_1 > n__g_1 > n__f_1 sel_2 > activate_1 > g_1 > n__g_1 > n__f_1 sel_2 > activate_1 > g_1 > 0 > n__f_1 sel_2 > activate_1 > g_1 > s_1 > n__f_1 Status: f_1: multiset status cons_2: multiset status n__f_1: multiset status n__g_1: multiset status g_1: multiset status 0: multiset status s_1: multiset status sel_2: [1,2] activate_1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(X) -> cons(X, n__f(n__g(X))) g(0) -> s(0) g(s(X)) -> s(s(g(X))) sel(0, cons(X, Y)) -> X sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) f(X) -> n__f(X) g(X) -> n__g(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(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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