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HRS union beta 16688 pair #381734563
details
property
value
status
complete
benchmark
ordrec.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
Mixed_HO_10
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.253342151642 seconds
cpu usage
0.241759737
max memory
1.8231296E7
stage attributes
key
value
output-size
2521
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: 0 : [] --> ord lim : [nat -> ord] --> ord rec : [ord * a * ord -> a -> a * nat -> ord -> nat -> a -> a] --> a s : [ord] --> ord Rules: rec(0, x, f, g) => x rec(s(x), y, f, g) => f x rec(x, y, f, g) rec(lim(f), x, g, h) => h f (/\y.rec(f y, x, g, h)) 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]). We thus obtain the following dependency pair problem (P_0, R_0, static, formative): Dependency Pairs P_0: 0] rec#(s(X), Y, F, G) =#> rec#(X, Y, F, G) 1] rec#(lim(F), X, G, H) =#> rec#(F Y, X, G, H) Rules R_0: rec(0, X, F, G) => X rec(s(X), Y, F, G) => F X rec(X, Y, F, G) rec(lim(F), X, G, H) => H F (/\x.rec(F x, X, G, H)) 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 apply the accessible subterm criterion with the following projection function: nu(rec#) = 1 Thus, we can orient the dependency pairs as follows: nu(rec#(s(X), Y, F, G)) = s(X) [>] X = nu(rec#(X, Y, F, G)) nu(rec#(lim(F), X, G, H)) = lim(F) [>] F Y = nu(rec#(F Y, X, G, H)) By [Kop13, Thm. 6], we may replace a dependency pair problem (P_0, R_0, static, f) by ({}, R_0, static, f). By the empty set processor [Kop12, Thm. 7.15] this problem may be immediately removed. 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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