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HRS union beta 16688 pair #381734332
details
property
value
status
complete
benchmark
kop12thesis_ex2.11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Kop_13
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.169188976288 seconds
cpu usage
0.164457731
max memory
8937472.0
stage attributes
key
value
output-size
8201
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 : [nat * list] --> list emap : [nat -> nat * list] --> list nil : [] --> list twice : [nat -> nat] --> nat -> nat Rules: emap(f, nil) => nil emap(f, cons(x, y)) => cons(f x, emap(/\z.twice(f) z, y)) twice(f) x => f (f x) 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]): emap(F, nil) >? nil emap(F, cons(X, Y)) >? cons(F X, emap(/\x.twice(F, x), Y)) twice(F, X) >? F (F X) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[emap(x_1, x_2)]] = emap(x_2, x_1) [[nil]] = _|_ We choose Lex = {emap} and Mul = {@_{o -> o}, cons, twice}, and the following precedence: emap > cons > twice > @_{o -> o} Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: emap(F, _|_) > _|_ emap(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), emap(/\x.twice(F, x), Y)) twice(F, X) >= @_{o -> o}(F, @_{o -> o}(F, X)) With these choices, we have: 1] emap(F, _|_) > _|_ because [2], by definition 2] emap*(F, _|_) >= _|_ by (Bot) 3] emap(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), emap(/\x.twice(F, x), Y)) because [4], by (Star) 4] emap*(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), emap(/\x.twice(F, x), Y)) because emap > cons, [5] and [12], by (Copy) 5] emap*(F, cons(X, Y)) >= @_{o -> o}(F, X) because emap > @_{o -> o}, [6] and [8], by (Copy) 6] emap*(F, cons(X, Y)) >= F because [7], by (Select) 7] F >= F by (Meta) 8] emap*(F, cons(X, Y)) >= X because [9], by (Select) 9] cons(X, Y) >= X because [10], by (Star) 10] cons*(X, Y) >= X because [11], by (Select) 11] X >= X by (Meta) 12] emap*(F, cons(X, Y)) >= emap(/\x.twice(F, x), Y) because [13], [16] and [21], by (Stat) 13] cons(X, Y) > Y because [14], by definition 14] cons*(X, Y) >= Y because [15], by (Select) 15] Y >= Y by (Meta) 16] emap*(F, cons(X, Y)) >= /\y.twice(F, y) because [17], by (F-Abs) 17] emap*(F, cons(X, Y), x) >= twice(F, x) because emap > twice, [18] and [19], by (Copy) 18] emap*(F, cons(X, Y), x) >= F because [7], by (Select) 19] emap*(F, cons(X, Y), x) >= x because [20], by (Select) 20] x >= x by (Var) 21] emap*(F, cons(X, Y)) >= Y because [22], by (Select) 22] cons(X, Y) >= Y because [14], by (Star) 23] twice(F, X) >= @_{o -> o}(F, @_{o -> o}(F, X)) because [24], by (Star) 24] twice*(F, X) >= @_{o -> o}(F, @_{o -> o}(F, X)) because twice > @_{o -> o}, [25] and [27], by (Copy) 25] twice*(F, X) >= F because [26], by (Select) 26] F >= F by (Meta) 27] twice*(F, X) >= @_{o -> o}(F, X) because twice > @_{o -> o}, [25] and [28], by (Copy) 28] twice*(F, X) >= X because [29], by (Select) 29] X >= X by (Meta) We can thus remove the following rules: emap(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]): emap(F, cons(X, Y)) >? cons(F X, emap(/\x.twice(F, x), Y)) twice(F, X) >? F (F X) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions:
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