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HRS union beta 16688 pair #381734893
details
property
value
status
complete
benchmark
Applicative_first_order_05__01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.0880048274994 seconds
cpu usage
0.084073899
max memory
4521984.0
stage attributes
key
value
output-size
5432
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: !fac3220 : [a * a] --> a !facdiv : [a * a] --> a !facdot : [a * a] --> a cons : [c * d] --> d e : [] --> a false : [] --> b filter : [c -> b * d] --> d filter2 : [b * c -> b * c * d] --> d map : [c -> c * d] --> d nil : [] --> d true : [] --> b Rules: !fac3220(x, x) => e !fac3220(e, x) => x !fac3220(x, !facdot(x, y)) => y !fac3220(!facdiv(x, y), x) => y !facdiv(x, x) => e !facdiv(x, e) => x !facdiv(!facdot(x, y), y) => x !facdiv(x, !fac3220(y, x)) => y !facdot(e, x) => x !facdot(x, e) => x !facdot(x, !fac3220(x, y)) => y !facdot(!facdiv(x, y), y) => x 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]): !fac3220(X, X) >? e !fac3220(e, X) >? X !fac3220(X, !facdot(X, Y)) >? Y !fac3220(!facdiv(X, Y), X) >? Y !facdiv(X, X) >? e !facdiv(X, e) >? X !facdiv(!facdot(X, Y), Y) >? X !facdiv(X, !fac3220(Y, X)) >? Y !facdot(e, X) >? X !facdot(X, e) >? X !facdot(X, !fac3220(X, Y)) >? Y !facdot(!facdiv(X, Y), Y) >? X 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) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: !fac3220 = \y0y1.3 + y0 + 2y1 !facdiv = \y0y1.3 + y0 + y1 !facdot = \y0y1.3 + y0 + 2y1 cons = \y0y1.3 + y0 + y1 e = 0 false = 3 filter = \G0y1.1 + 3y1 + 2G0(0) + 3y1G0(y1) filter2 = \y0G1y2y3.y2 + 2y0 + 3y3 + G1(0) + G1(y2) + 3y3G1(y3) map = \G0y1.3y1 + G0(y1) + 2y1G0(y1) nil = 0 true = 3 Using this interpretation, the requirements translate to: [[!fac3220(_x0, _x0)]] = 3 + 3x0 > 0 = [[e]] [[!fac3220(e, _x0)]] = 3 + 2x0 > x0 = [[_x0]] [[!fac3220(_x0, !facdot(_x0, _x1))]] = 9 + 3x0 + 4x1 > x1 = [[_x1]] [[!fac3220(!facdiv(_x0, _x1), _x0)]] = 6 + x1 + 3x0 > x1 = [[_x1]] [[!facdiv(_x0, _x0)]] = 3 + 2x0 > 0 = [[e]] [[!facdiv(_x0, e)]] = 3 + x0 > x0 = [[_x0]] [[!facdiv(!facdot(_x0, _x1), _x1)]] = 6 + x0 + 3x1 > x0 = [[_x0]] [[!facdiv(_x0, !fac3220(_x1, _x0))]] = 6 + x1 + 3x0 > x1 = [[_x1]] [[!facdot(e, _x0)]] = 3 + 2x0 > x0 = [[_x0]] [[!facdot(_x0, e)]] = 3 + x0 > x0 = [[_x0]] [[!facdot(_x0, !fac3220(_x0, _x1))]] = 9 + 3x0 + 4x1 > x1 = [[_x1]] [[!facdot(!facdiv(_x0, _x1), _x1)]] = 6 + x0 + 3x1 > x0 = [[_x0]] [[map(_F0, nil)]] = F0(0) >= 0 = [[nil]]
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