details

property	value
status	complete
benchmark	AotoYamada_05__022.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.0485048294067 seconds
cpu usage	0.044333963
max memory	2785280.0

stage attributes

key	value
output-size	2938
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 : [b * c] --> c leaf : [a] --> b mapt : [a -> a * b] --> b maptlist : [a -> a * c] --> c nil : [] --> c node : [c] --> b Rules: mapt(f, leaf(x)) => leaf(f x) mapt(f, node(x)) => node(maptlist(f, x)) maptlist(f, nil) => nil maptlist(f, cons(x, y)) => cons(mapt(f, x), maptlist(f, y)) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): mapt(F, leaf(X)) >? leaf(F X) mapt(F, node(X)) >? node(maptlist(F, X)) maptlist(F, nil) >? nil maptlist(F, cons(X, Y)) >? cons(mapt(F, X), maptlist(F, Y)) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: cons = \y0y1.2 + y1 + 2y0 leaf = \y0.y0 mapt = \G0y1.1 + 3y1 + G0(y1) + 2y1G0(y1) maptlist = \G0y1.3y1 + G0(0) + G0(y1) + 2y1G0(y1) nil = 0 node = \y0.1 + y0 Using this interpretation, the requirements translate to: [[mapt(_F0, leaf(_x1))]] = 1 + 3x1 + F0(x1) + 2x1F0(x1) > x1 + F0(x1) = [[leaf(_F0 _x1)]] [[mapt(_F0, node(_x1))]] = 4 + 3x1 + 2x1F0(1 + x1) + 3F0(1 + x1) > 1 + 3x1 + F0(0) + F0(x1) + 2x1F0(x1) = [[node(maptlist(_F0, _x1))]] [[maptlist(_F0, nil)]] = 2F0(0) >= 0 = [[nil]] [[maptlist(_F0, cons(_x1, _x2))]] = 6 + 3x2 + 6x1 + F0(0) + 2x2F0(2 + x2 + 2x1) + 4x1F0(2 + x2 + 2x1) + 5F0(2 + x2 + 2x1) > 4 + 3x2 + 6x1 + F0(0) + F0(x2) + 2x2F0(x2) + 2F0(x1) + 4x1F0(x1) = [[cons(mapt(_F0, _x1), maptlist(_F0, _x2))]] We can thus remove the following rules: mapt(F, leaf(X)) => leaf(F X) mapt(F, node(X)) => node(maptlist(F, X)) maptlist(F, cons(X, Y)) => cons(mapt(F, X), maptlist(F, Y)) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): maptlist(F, nil) >? nil We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: maptlist = \G0y1.3 + 3y1 + G0(0) nil = 0 Using this interpretation, the requirements translate to: [[maptlist(_F0, nil)]] = 3 + F0(0) > 0 = [[nil]] We can thus remove the following rules: maptlist(F, nil) => nil 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 +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. popout

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actions

all output return to HRS union beta 16688