Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
HRS union beta 16688 pair #381734267
details
property
value
status
complete
benchmark
kripke.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n040.star.cs.uiowa.edu
space
Hamana_17
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.678255081177 seconds
cpu usage
1.349838125
max memory
9.5903744E7
stage attributes
key
value
output-size
5725
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: abs : [] --> a -> b -> Arrab app : [] --> Arrab -> a -> b box : [] --> a -> Boxa unbox : [] --> Boxa -> a Rules: app (abs (/\x.f x)) y => f y abs (/\x.app y x) => y unbox (box x) => x box (unbox x) => x Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term. We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0). This leads to the following AFSM: Alphabet: abs : [a -> b] --> Arrab app : [Arrab * a] --> b box : [a] --> Boxa unbox : [Boxa] --> a ~AP1 : [a -> b * a] --> b Rules: app(abs(/\x.~AP1(F, x)), X) => ~AP1(F, X) abs(/\x.app(X, x)) => X unbox(box(X)) => X box(unbox(X)) => X app(abs(/\x.app(X, x)), Y) => app(X, Y) ~AP1(F, X) => F X We observe that the rules contain a first-order subset: unbox(box(X)) => X box(unbox(X)) => X Moreover, the system is finitely branching. Thus, by [Kop12, Thm. 7.55], we may omit all first-order dependency pairs from the dependency pair problem (DP(R), R) if this first-order part is Ce-terminating when seen as a many-sorted first-order TRS. According to the external first-order termination prover, this system is indeed Ce-terminating: || proof of resources/system.trs || # AProVE Commit ID: d84c10301d352dfd14de2104819581f4682260f5 fuhs 20130616 || || || Termination w.r.t. Q of the given QTRS could be proven: || || (0) QTRS || (1) QTRSRRRProof [EQUIVALENT] || (2) QTRS || (3) RisEmptyProof [EQUIVALENT] || (4) YES || || || ---------------------------------------- || || (0) || Obligation: || Q restricted rewrite system: || The TRS R consists of the following rules: || || unbox(box(%X)) -> %X || box(unbox(%X)) -> %X || ~PAIR(%X, %Y) -> %X || ~PAIR(%X, %Y) -> %Y || || Q is empty. || || ---------------------------------------- || || (1) QTRSRRRProof (EQUIVALENT) || Used ordering: || Polynomial interpretation [POLO]: || || POL(box(x_1)) = 2 + x_1 || POL(unbox(x_1)) = 1 + 2*x_1 || POL(~PAIR(x_1, x_2)) = 2 + x_1 + x_2 || With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: || || unbox(box(%X)) -> %X || box(unbox(%X)) -> %X || ~PAIR(%X, %Y) -> %X || ~PAIR(%X, %Y) -> %Y || || || || || ----------------------------------------
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to HRS union beta 16688