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TRS Standard pair #516962250
details
property
value
status
complete
benchmark
Ex4_7_15_Bor03_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n061.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.39788198471 seconds
cpu usage
6.245675788
max memory
4.96791552E8
stage attributes
key
value
output-size
5834
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 91 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 7 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 0 ms] (10) QTRS (11) AAECC Innermost [EQUIVALENT, 0 ms] (12) QTRS (13) DependencyPairsProof [EQUIVALENT, 0 ms] (14) QDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(0) -> cons(0, n__f(n__s(n__0))) f(s(0)) -> f(p(s(0))) p(s(0)) -> 0 f(X) -> n__f(X) s(X) -> n__s(X) 0 -> n__0 activate(n__f(X)) -> f(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__0) -> 0 activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 1 POL(activate(x_1)) = 2 + 2*x_1 POL(cons(x_1, x_2)) = x_1 + x_2 POL(f(x_1)) = 2 + 2*x_1 POL(n__0) = 0 POL(n__f(x_1)) = 2 + 2*x_1 POL(n__s(x_1)) = x_1 POL(p(x_1)) = x_1 POL(s(x_1)) = x_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(n__s(n__0))) 0 -> n__0 activate(n__0) -> 0 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 f(X) -> n__f(X) s(X) -> n__s(X) activate(n__f(X)) -> f(activate(X)) activate(n__s(X)) -> s(activate(X)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 1
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