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TRS Stand 20472 pair #381715827
details
property
value
status
complete
benchmark
ExProp7_Luc06_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n027.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.6748008728 seconds
cpu usage
3.904397335
max memory
2.36843008E8
stage attributes
key
value
output-size
3390
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 67 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) AAECC Innermost [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 6 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(X)) -> X 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: activate_1 > [f_1, 0] > cons_2 Status: f_1: [1] 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(X)) -> X Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(f(x_1)) = 2*x_1 POL(p(x_1)) = x_1 POL(s(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: p(s(X)) -> X
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