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HRS union beta 16688 pair #381734744
details
property
value
status
complete
benchmark
Applicative_05__TreeMap.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.259917020798 seconds
cpu usage
0.256348729
max memory
1.3733888E7
stage attributes
key
value
output-size
7414
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 : [c * b] --> b map : [c -> c * b] --> b nil : [] --> b node : [a * b] --> c treemap : [a -> a] --> c -> c Rules: map(f, nil) => nil map(f, cons(x, y)) => cons(f x, map(f, y)) treemap(f) node(x, y) => node(f x, map(treemap(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]): map(F, nil) >? nil map(F, cons(X, Y)) >? cons(F X, map(F, Y)) treemap(F) node(X, Y) >? node(F X, map(treemap(F), Y)) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[nil]] = _|_ We choose Lex = {} and Mul = {@_{o -> o}, cons, map, node, treemap}, and the following precedence: treemap > @_{o -> o} = map > cons > node Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: map(F, _|_) > _|_ map(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) @_{o -> o}(treemap(F), node(X, Y)) >= node(@_{o -> o}(F, X), map(treemap(F), Y)) With these choices, we have: 1] map(F, _|_) > _|_ because [2], by definition 2] map*(F, _|_) >= _|_ by (Bot) 3] map(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) because [4], by (Star) 4] map*(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) because map > cons, [5] and [10], by (Copy) 5] map*(F, cons(X, Y)) >= @_{o -> o}(F, X) because map = @_{o -> o}, map in Mul, [6] and [7], by (Stat) 6] F >= F by (Meta) 7] cons(X, Y) > X because [8], by definition 8] cons*(X, Y) >= X because [9], by (Select) 9] X >= X by (Meta) 10] map*(F, cons(X, Y)) >= map(F, Y) because map in Mul, [6] and [11], by (Stat) 11] cons(X, Y) > Y because [12], by definition 12] cons*(X, Y) >= Y because [13], by (Select) 13] Y >= Y by (Meta) 14] @_{o -> o}(treemap(F), node(X, Y)) >= node(@_{o -> o}(F, X), map(treemap(F), Y)) because [15], by (Star) 15] @_{o -> o}*(treemap(F), node(X, Y)) >= node(@_{o -> o}(F, X), map(treemap(F), Y)) because [16], by (Select) 16] treemap(F) @_{o -> o}*(treemap(F), node(X, Y)) >= node(@_{o -> o}(F, X), map(treemap(F), Y)) because [17] 17] treemap*(F, @_{o -> o}*(treemap(F), node(X, Y))) >= node(@_{o -> o}(F, X), map(treemap(F), Y)) because treemap > node, [18] and [29], by (Copy) 18] treemap*(F, @_{o -> o}*(treemap(F), node(X, Y))) >= @_{o -> o}(F, X) because treemap > @_{o -> o}, [19] and [21], by (Copy) 19] treemap*(F, @_{o -> o}*(treemap(F), node(X, Y))) >= F because [20], by (Select) 20] F >= F by (Meta) 21] treemap*(F, @_{o -> o}*(treemap(F), node(X, Y))) >= X because [22], by (Select) 22] @_{o -> o}*(treemap(F), node(X, Y)) >= X because [23], by (Select) 23] treemap(F) @_{o -> o}*(treemap(F), node(X, Y)) >= X because [24] 24] treemap*(F, @_{o -> o}*(treemap(F), node(X, Y))) >= X because [25], by (Select) 25] @_{o -> o}*(treemap(F), node(X, Y)) >= X because [26], by (Select) 26] node(X, Y) >= X because [27], by (Star) 27] node*(X, Y) >= X because [28], by (Select) 28] X >= X by (Meta) 29] treemap*(F, @_{o -> o}*(treemap(F), node(X, Y))) >= map(treemap(F), Y) because [30], by (Select) 30] @_{o -> o}*(treemap(F), node(X, Y)) >= map(treemap(F), Y) because @_{o -> o} = map, @_{o -> o} in Mul, [31] and [33], by (Stat) 31] treemap(F) >= treemap(F) because treemap in Mul and [32], by (Fun) 32] F >= F by (Meta) 33] node(X, Y) > Y because [34], by definition 34] node*(X, Y) >= Y because [35], by (Select) 35] Y >= Y by (Meta) We can thus remove the following rules: map(F, nil) => nil We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): map(F, cons(X, Y)) >? cons(F X, map(F, Y)) treemap(F) node(X, Y) >? node(F X, map(treemap(F), Y))
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