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HRS union beta 16688 pair #381734926
details
property
value
status
complete
benchmark
Applicative_first_order_05__30.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n022.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.335203886032 seconds
cpu usage
0.332362308
max memory
1.4741504E7
stage attributes
key
value
output-size
15908
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: !faccolon : [a * a] --> a C : [] --> a cons : [c * d] --> d false : [] --> b filter : [c -> b * d] --> d filter2 : [b * c -> b * c * d] --> d map : [c -> c * d] --> d nil : [] --> d true : [] --> b Rules: !faccolon(!faccolon(!faccolon(!faccolon(C, x), y), z), u) => !faccolon(!faccolon(x, z), !faccolon(!faccolon(!faccolon(x, y), z), u)) 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]): !faccolon(!faccolon(!faccolon(!faccolon(C, X), Y), Z), U) >? !faccolon(!faccolon(X, Z), !faccolon(!faccolon(!faccolon(X, Y), Z), U)) 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 = {!faccolon, @_{o -> o}, filter, filter2} and Mul = {C, cons, false, map, true}, and the following precedence: map > C > !faccolon > false > @_{o -> o} = filter = filter2 > true > cons Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: !faccolon(!faccolon(!faccolon(!faccolon(C, X), Y), Z), U) >= !faccolon(!faccolon(X, Z), !faccolon(!faccolon(!faccolon(X, Y), Z), U)) 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] !faccolon(!faccolon(!faccolon(!faccolon(C, X), Y), Z), U) >= !faccolon(!faccolon(X, Z), !faccolon(!faccolon(!faccolon(X, Y), Z), U)) because [2], by (Star) 2] !faccolon*(!faccolon(!faccolon(!faccolon(C, X), Y), Z), U) >= !faccolon(!faccolon(X, Z), !faccolon(!faccolon(!faccolon(X, Y), Z), U)) because [3], [14] and [18], by (Stat) 3] !faccolon(!faccolon(!faccolon(C, X), Y), Z) > !faccolon(X, Z) because [4], by definition 4] !faccolon*(!faccolon(!faccolon(C, X), Y), Z) >= !faccolon(X, Z) because [5], [10] and [12], by (Stat) 5] !faccolon(!faccolon(C, X), Y) > X because [6], by definition 6] !faccolon*(!faccolon(C, X), Y) >= X because [7], by (Select) 7] !faccolon(C, X) >= X because [8], by (Star) 8] !faccolon*(C, X) >= X because [9], by (Select) 9] X >= X by (Meta) 10] !faccolon*(!faccolon(!faccolon(C, X), Y), Z) >= X because [11], by (Select) 11] !faccolon(!faccolon(C, X), Y) >= X because [6], by (Star) 12] !faccolon*(!faccolon(!faccolon(C, X), Y), Z) >= Z because [13], by (Select) 13] Z >= Z by (Meta) 14] !faccolon*(!faccolon(!faccolon(!faccolon(C, X), Y), Z), U) >= !faccolon(X, Z) because [15], by (Select) 15] !faccolon(!faccolon(!faccolon(C, X), Y), Z) >= !faccolon(X, Z) because [16] and [17], by (Fun) 16] !faccolon(!faccolon(C, X), Y) >= X because [6], by (Star) 17] Z >= Z by (Meta) 18] !faccolon*(!faccolon(!faccolon(!faccolon(C, X), Y), Z), U) >= !faccolon(!faccolon(!faccolon(X, Y), Z), U) because [19], [31] and [34], by (Stat) 19] !faccolon(!faccolon(!faccolon(C, X), Y), Z) > !faccolon(!faccolon(X, Y), Z) because [20], by definition 20] !faccolon*(!faccolon(!faccolon(C, X), Y), Z) >= !faccolon(!faccolon(X, Y), Z) because [21], [27] and [12], by (Stat) 21] !faccolon(!faccolon(C, X), Y) > !faccolon(X, Y) because [22], by definition 22] !faccolon*(!faccolon(C, X), Y) >= !faccolon(X, Y) because [23], [6] and [25], by (Stat) 23] !faccolon(C, X) > X because [24], by definition 24] !faccolon*(C, X) >= X because [9], by (Select) 25] !faccolon*(!faccolon(C, X), Y) >= Y because [26], by (Select) 26] Y >= Y by (Meta) 27] !faccolon*(!faccolon(!faccolon(C, X), Y), Z) >= !faccolon(X, Y) because [28], by (Select) 28] !faccolon(!faccolon(C, X), Y) >= !faccolon(X, Y) because [29] and [30], by (Fun) 29] !faccolon(C, X) >= X because [24], by (Star) 30] Y >= Y by (Meta) 31] !faccolon*(!faccolon(!faccolon(!faccolon(C, X), Y), Z), U) >= !faccolon(!faccolon(X, Y), Z) because [32], by (Select) 32] !faccolon(!faccolon(!faccolon(C, X), Y), Z) >= !faccolon(!faccolon(X, Y), Z) because [33] and [17], by (Fun)
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