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HRS union beta 16688 pair #381734311
details
property
value
status
complete
benchmark
kop12lmcs2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
Kop_13
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.069228887558 seconds
cpu usage
0.06640555
max memory
4952064.0
stage attributes
key
value
output-size
2574
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: cons : [nat -> nat * funlist] --> funlist false : [] --> bool head : [funlist] --> nat -> nat if : [bool * nat -> string * nat -> string] --> nat -> string nil : [] --> funlist s : [nat] --> nat tail : [funlist] --> funlist test : [nat -> nat] --> bool true : [] --> bool Rules: if(true, f, g) => f if(false, f, g) => g test(/\x.s(x)) => true head(cons(f, x)) => f tail(cons(f, x)) => x This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs and accessible arguments in [Kop13]). In order to do so, we start by eta-expanding the system, which gives: if(true, F, G, X) => F X if(false, F, G, X) => G X test(/\x.s(x)) => true head(cons(F, X), Y) => F Y tail(cons(F, X)) => X We thus obtain the following dependency pair problem (P_0, R_0, static, formative): Dependency Pairs P_0: Rules R_0: if(true, F, G, X) => F X if(false, F, G, X) => G X test(/\x.s(x)) => true head(cons(F, X), Y) => F Y tail(cons(F, X)) => X Thus, the original system is terminating if (P_0, R_0, static, formative) is finite. We consider the dependency pair problem (P_0, R_0, static, formative). We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows: This graph has no strongly connected components. By [Kop12, Thm. 7.31], this implies finiteness of the dependency pair problem. As all dependency pair problems were succesfully simplified with sound (and complete) processors until nothing remained, we conclude termination. +++ Citations +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. [Kop13] C. Kop. Static Dependency Pairs with Accessibility. Unpublished manuscript, http://cl-informatik.uibk.ac.at/users/kop/static.pdf, 2013. [KusIsoSakBla09] K. Kusakari, Y. Isogai, M. Sakai, and F. Blanqui. Static Dependency Pair Method Based On Strong Computability for Higher-Order Rewrite Systems. In volume 92(10) of IEICE Transactions on Information and Systems. 2007--2015, 2009.
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