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TRS Standard pair #516963320
details
property
value
status
complete
benchmark
Ex4_7_15_Bor03_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n173.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.22255206108 seconds
cpu usage
5.662349158
max memory
4.71523328E8
stage attributes
key
value
output-size
3401
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 88 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) AAECC Innermost [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(0) -> cons(0, n__f(s(0))) f(s(0)) -> f(p(s(0))) p(s(0)) -> 0 f(X) -> n__f(X) activate(n__f(X)) -> f(X) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: f/1(YES) 0/0) cons/2(YES,YES) n__f/1)YES( s/1)YES( p/1)YES( activate/1(YES) Quasi precedence: 0 > f_1 > cons_2 activate_1 > f_1 > cons_2 Status: f_1: multiset status 0: multiset status cons_2: multiset status activate_1: [1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(0) -> cons(0, n__f(s(0))) f(X) -> n__f(X) activate(n__f(X)) -> f(X) activate(X) -> X ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(s(0)) -> f(p(s(0))) p(s(0)) -> 0 Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 2 POL(f(x_1)) = 2*x_1 POL(p(x_1)) = x_1 POL(s(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: p(s(0)) -> 0
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