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HRS union beta 16688 pair #381734917
details
property
value
status
complete
benchmark
Applicative_first_order_05__18.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n095.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.14839220047 seconds
cpu usage
0.14583357
max memory
8138752.0
stage attributes
key
value
output-size
7917
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: !facplus : [b * b] --> b !factimes : [a * b] --> b cons : [d * e] --> e false : [] --> c filter : [d -> c * e] --> e filter2 : [c * d -> c * d * e] --> e map : [d -> d * e] --> e nil : [] --> e true : [] --> c Rules: !factimes(x, !facplus(y, z)) => !facplus(!factimes(x, y), !factimes(x, z)) map(f, nil) => nil map(f, cons(x, y)) => cons(f x, map(f, y)) filter(f, nil) => nil filter(f, cons(x, y)) => filter2(f x, f, x, y) filter2(true, f, x, y) => cons(x, filter(f, y)) filter2(false, f, x, y) => filter(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]): !factimes(X, !facplus(Y, Z)) >? !facplus(!factimes(X, Y), !factimes(X, Z)) map(F, nil) >? nil map(F, cons(X, Y)) >? cons(F X, map(F, Y)) filter(F, nil) >? nil filter(F, cons(X, Y)) >? filter2(F X, F, X, Y) filter2(true, F, X, Y) >? cons(X, filter(F, Y)) filter2(false, F, X, Y) >? filter(F, Y) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[filter2(x_1, x_2, x_3, x_4)]] = filter2(x_2, x_4, x_1, x_3) [[nil]] = _|_ We choose Lex = {@_{o -> o}, filter, filter2} and Mul = {!facplus, !factimes, cons, false, map, true}, and the following precedence: map > false > @_{o -> o} = filter = filter2 > !factimes > !facplus > cons > true Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: !factimes(X, !facplus(Y, Z)) > !facplus(!factimes(X, Y), !factimes(X, Z)) map(F, _|_) >= _|_ map(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) filter(F, _|_) >= _|_ filter(F, cons(X, Y)) >= filter2(@_{o -> o}(F, X), F, X, Y) filter2(true, F, X, Y) >= cons(X, filter(F, Y)) filter2(false, F, X, Y) > filter(F, Y) With these choices, we have: 1] !factimes(X, !facplus(Y, Z)) > !facplus(!factimes(X, Y), !factimes(X, Z)) because [2], by definition 2] !factimes*(X, !facplus(Y, Z)) >= !facplus(!factimes(X, Y), !factimes(X, Z)) because !factimes > !facplus, [3] and [8], by (Copy) 3] !factimes*(X, !facplus(Y, Z)) >= !factimes(X, Y) because !factimes in Mul, [4] and [5], by (Stat) 4] X >= X by (Meta) 5] !facplus(Y, Z) > Y because [6], by definition 6] !facplus*(Y, Z) >= Y because [7], by (Select) 7] Y >= Y by (Meta) 8] !factimes*(X, !facplus(Y, Z)) >= !factimes(X, Z) because !factimes in Mul, [4] and [9], by (Stat) 9] !facplus(Y, Z) > Z because [10], by definition 10] !facplus*(Y, Z) >= Z because [11], by (Select) 11] Z >= Z by (Meta) 12] map(F, _|_) >= _|_ by (Bot) 13] map(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) because [14], by (Star) 14] map*(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) because map > cons, [15] and [22], by (Copy) 15] map*(F, cons(X, Y)) >= @_{o -> o}(F, X) because map > @_{o -> o}, [16] and [18], by (Copy) 16] map*(F, cons(X, Y)) >= F because [17], by (Select) 17] F >= F by (Meta) 18] map*(F, cons(X, Y)) >= X because [19], by (Select) 19] cons(X, Y) >= X because [20], by (Star) 20] cons*(X, Y) >= X because [21], by (Select) 21] X >= X by (Meta) 22] map*(F, cons(X, Y)) >= map(F, Y) because map in Mul, [23] and [24], by (Stat) 23] F >= F by (Meta) 24] cons(X, Y) > Y because [25], by definition 25] cons*(X, Y) >= Y because [26], by (Select) 26] Y >= Y by (Meta) 27] filter(F, _|_) >= _|_ by (Bot) 28] filter(F, cons(X, Y)) >= filter2(@_{o -> o}(F, X), F, X, Y) because [29], by (Star)
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