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HRS union beta 16688 pair #381734684
details
property
value
status
complete
benchmark
Applicative_05__Ex9Maps.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n107.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
4.71490001678 seconds
cpu usage
4.693560637
max memory
2.00265728E8
stage attributes
key
value
output-size
11767
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: cons : [d * e] --> e g : [] --> b map!fac62201 : [d -> d * e] --> e map!fac62202 : [d -> a -> d * a * e] --> e map!fac62203 : [b -> d -> c -> d * b * c * e] --> e Rules: map!fac62201(f, cons(x, y)) => cons(f x, map!fac62201(f, y)) map!fac62202(f, x, cons(y, z)) => cons(f y x, map!fac62202(f, x, z)) map!fac62203(f, g, x, cons(y, z)) => cons(f g y x, map!fac62203(f, g, x, z)) 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!fac62201(F, cons(X, Y)) >? cons(F X, map!fac62201(F, Y)) map!fac62202(F, X, cons(Y, Z)) >? cons(F Y X, map!fac62202(F, X, Z)) map!fac62203(F, g, X, cons(Y, Z)) >? cons(F g Y X, map!fac62203(F, g, X, Z)) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[g]] = _|_ We choose Lex = {} and Mul = {@_{o -> o -> o -> o}, @_{o -> o -> o}, @_{o -> o}, cons, map!fac62201, map!fac62202, map!fac62203}, and the following precedence: map!fac62201 > map!fac62203 > @_{o -> o -> o} = map!fac62202 > @_{o -> o} > cons > @_{o -> o -> o -> o} Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: map!fac62201(F, cons(X, Y)) > cons(@_{o -> o}(F, X), map!fac62201(F, Y)) map!fac62202(F, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(F, Y), X), map!fac62202(F, X, Z)) map!fac62203(F, _|_, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y), X), map!fac62203(F, _|_, X, Z)) With these choices, we have: 1] map!fac62201(F, cons(X, Y)) > cons(@_{o -> o}(F, X), map!fac62201(F, Y)) because [2], by definition 2] map!fac62201*(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map!fac62201(F, Y)) because map!fac62201 > cons, [3] and [10], by (Copy) 3] map!fac62201*(F, cons(X, Y)) >= @_{o -> o}(F, X) because map!fac62201 > @_{o -> o}, [4] and [6], by (Copy) 4] map!fac62201*(F, cons(X, Y)) >= F because [5], by (Select) 5] F >= F by (Meta) 6] map!fac62201*(F, cons(X, Y)) >= X because [7], by (Select) 7] cons(X, Y) >= X because [8], by (Star) 8] cons*(X, Y) >= X because [9], by (Select) 9] X >= X by (Meta) 10] map!fac62201*(F, cons(X, Y)) >= map!fac62201(F, Y) because map!fac62201 in Mul, [11] and [12], by (Stat) 11] F >= F by (Meta) 12] cons(X, Y) > Y because [13], by definition 13] cons*(X, Y) >= Y because [14], by (Select) 14] Y >= Y by (Meta) 15] map!fac62202(F, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(F, Y), X), map!fac62202(F, X, Z)) because [16], by (Star) 16] map!fac62202*(F, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(F, Y), X), map!fac62202(F, X, Z)) because map!fac62202 > cons, [17] and [25], by (Copy) 17] map!fac62202*(F, X, cons(Y, Z)) >= @_{o -> o}(@_{o -> o -> o}(F, Y), X) because map!fac62202 > @_{o -> o}, [18] and [23], by (Copy) 18] map!fac62202*(F, X, cons(Y, Z)) >= @_{o -> o -> o}(F, Y) because map!fac62202 = @_{o -> o -> o}, map!fac62202 in Mul, [19] and [20], by (Stat) 19] F >= F by (Meta) 20] cons(Y, Z) > Y because [21], by definition 21] cons*(Y, Z) >= Y because [22], by (Select) 22] Y >= Y by (Meta) 23] map!fac62202*(F, X, cons(Y, Z)) >= X because [24], by (Select) 24] X >= X by (Meta) 25] map!fac62202*(F, X, cons(Y, Z)) >= map!fac62202(F, X, Z) because map!fac62202 in Mul, [19], [26] and [27], by (Stat) 26] X >= X by (Meta) 27] cons(Y, Z) > Z because [28], by definition 28] cons*(Y, Z) >= Z because [29], by (Select) 29] Z >= Z by (Meta) 30] map!fac62203(F, _|_, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y), X), map!fac62203(F, _|_, X, Z)) because [31], by (Star) 31] map!fac62203*(F, _|_, X, cons(Y, Z)) >= cons(@_{o -> o}(@_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y), X), map!fac62203(F, _|_, X, Z)) because map!fac62203 > cons, [32] and [44], by (Copy) 32] map!fac62203*(F, _|_, X, cons(Y, Z)) >= @_{o -> o}(@_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y), X) because map!fac62203 > @_{o -> o}, [33] and [42], by (Copy) 33] map!fac62203*(F, _|_, X, cons(Y, Z)) >= @_{o -> o -> o}(@_{o -> o -> o -> o}(F, _|_), Y) because map!fac62203 > @_{o -> o -> o}, [34] and [38], by (Copy) 34] map!fac62203*(F, _|_, X, cons(Y, Z)) >= @_{o -> o -> o -> o}(F, _|_) because map!fac62203 > @_{o -> o -> o -> o}, [35] and [37], by (Copy) 35] map!fac62203*(F, _|_, X, cons(Y, Z)) >= F because [36], by (Select) 36] F >= F by (Meta) 37] map!fac62203*(F, _|_, X, cons(Y, Z)) >= _|_ by (Bot) 38] map!fac62203*(F, _|_, X, cons(Y, Z)) >= Y because [39], by (Select) 39] cons(Y, Z) >= Y because [40], by (Star) 40] cons*(Y, Z) >= Y because [41], by (Select) 41] Y >= Y by (Meta) 42] map!fac62203*(F, _|_, X, cons(Y, Z)) >= X because [43], by (Select) 43] X >= X by (Meta) 44] map!fac62203*(F, _|_, X, cons(Y, Z)) >= map!fac62203(F, _|_, X, Z) because map!fac62203 in Mul, [45], [46], [47] and [48], by (Stat) 45] F >= F by (Meta) 46] _|_ >= _|_ by (Bot) 47] X >= X by (Meta)
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