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HRS union beta 16688 pair #381734263
details
property
value
status
complete
benchmark
kop11cai2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n191.star.cs.uiowa.edu
space
Kop_13
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.0183320045471 seconds
cpu usage
0.015451257
max memory
1343488.0
stage attributes
key
value
output-size
2154
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: pair : [nat -> nat * nat] --> nat split : [nat] --> nat Rules: split(f x) => pair(f, 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: pair : [nat -> nat * nat] --> nat split : [nat] --> nat ~AP1 : [nat -> nat * nat] --> nat Rules: split(~AP1(F, X)) => pair(F, X) ~AP1(F, X) => F X We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): split(~AP1(F, X)) >? pair(F, X) ~AP1(F, X) >? F X We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: pair = \G0y1.y1 + G0(0) split = \y0.3 + 3y0 ~AP1 = \G0y1.3 + 3y1 + 3G0(0) + 3G0(y1) Using this interpretation, the requirements translate to: [[split(~AP1(_F0, _x1))]] = 12 + 9x1 + 9F0(0) + 9F0(x1) > x1 + F0(0) = [[pair(_F0, _x1)]] [[~AP1(_F0, _x1)]] = 3 + 3x1 + 3F0(0) + 3F0(x1) > x1 + F0(x1) = [[_F0 _x1]] We can thus remove the following rules: split(~AP1(F, X)) => pair(F, X) ~AP1(F, X) => F X All rules were succesfully removed. Thus, termination of the original system has been reduced to termination of the beta-rule, which is well-known to hold. +++ Citations +++ [Kop11] C. Kop. Simplifying Algebraic Functional Systems. In Proceedings of CAI 2011, volume 6742 of LNCS. 201--215, Springer, 2011. [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012.
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