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HRS union beta 16688 pair #381734413
details
property
value
status
complete
benchmark
AotoYamada_05__014.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n016.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.320006132126 seconds
cpu usage
0.224415058
max memory
1.1628544E7
stage attributes
key
value
output-size
8916
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: 0 : [] --> b cons : [b * a] --> a double : [] --> a -> a inc : [] --> a -> a map : [b -> b] --> a -> a nil : [] --> a plus : [b] --> b -> b s : [b] --> b times : [b] --> b -> b Rules: plus(0) x => x plus(s(x)) y => s(plus(x) y) times(0) x => 0 times(s(x)) y => plus(times(x) y) y map(f) nil => nil map(f) cons(x, y) => cons(f x, map(f) y) inc => map(plus(s(0))) double => map(times(s(s(0)))) 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]): plus(0) X >? X plus(s(X)) Y >? s(plus(X) Y) times(0) X >? 0 times(s(X)) Y >? plus(times(X) Y) Y map(F) nil >? nil map(F) cons(X, Y) >? cons(F X, map(F) Y) inc >? map(plus(s(0))) double >? map(times(s(s(0)))) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[0]] = _|_ [[nil]] = _|_ We choose Lex = {} and Mul = {@_{o -> o}, cons, double, inc, map, plus, s, times}, and the following precedence: double > inc > map > times > plus > s > cons > @_{o -> o} Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: @_{o -> o}(plus(_|_), X) >= X @_{o -> o}(plus(s(X)), Y) > s(@_{o -> o}(plus(X), Y)) @_{o -> o}(times(_|_), X) >= _|_ @_{o -> o}(times(s(X)), Y) > @_{o -> o}(plus(@_{o -> o}(times(X), Y)), Y) @_{o -> o}(map(F), _|_) >= _|_ @_{o -> o}(map(F), cons(X, Y)) > cons(@_{o -> o}(F, X), @_{o -> o}(map(F), Y)) inc >= map(plus(s(_|_))) double >= map(times(s(s(_|_)))) With these choices, we have: 1] @_{o -> o}(plus(_|_), X) >= X because [2], by (Star) 2] @_{o -> o}*(plus(_|_), X) >= X because [3], by (Select) 3] X >= X by (Meta) 4] @_{o -> o}(plus(s(X)), Y) > s(@_{o -> o}(plus(X), Y)) because [5], by definition 5] @_{o -> o}*(plus(s(X)), Y) >= s(@_{o -> o}(plus(X), Y)) because [6], by (Select) 6] plus(s(X)) @_{o -> o}*(plus(s(X)), Y) >= s(@_{o -> o}(plus(X), Y)) because [7] 7] plus*(s(X), @_{o -> o}*(plus(s(X)), Y)) >= s(@_{o -> o}(plus(X), Y)) because plus > s and [8], by (Copy) 8] plus*(s(X), @_{o -> o}*(plus(s(X)), Y)) >= @_{o -> o}(plus(X), Y) because plus > @_{o -> o}, [9] and [13], by (Copy) 9] plus*(s(X), @_{o -> o}*(plus(s(X)), Y)) >= plus(X) because plus in Mul and [10], by (Stat) 10] s(X) > X because [11], by definition 11] s*(X) >= X because [12], by (Select) 12] X >= X by (Meta) 13] plus*(s(X), @_{o -> o}*(plus(s(X)), Y)) >= Y because [14], by (Select) 14] @_{o -> o}*(plus(s(X)), Y) >= Y because [15], by (Select) 15] plus(s(X)) @_{o -> o}*(plus(s(X)), Y) >= Y because [16] 16] plus*(s(X), @_{o -> o}*(plus(s(X)), Y)) >= Y because [17], by (Select) 17] @_{o -> o}*(plus(s(X)), Y) >= Y because [18], by (Select) 18] Y >= Y by (Meta) 19] @_{o -> o}(times(_|_), X) >= _|_ by (Bot) 20] @_{o -> o}(times(s(X)), Y) > @_{o -> o}(plus(@_{o -> o}(times(X), Y)), Y) because [21], by definition 21] @_{o -> o}*(times(s(X)), Y) >= @_{o -> o}(plus(@_{o -> o}(times(X), Y)), Y) because [22], by (Select) 22] times(s(X)) @_{o -> o}*(times(s(X)), Y) >= @_{o -> o}(plus(@_{o -> o}(times(X), Y)), Y) because [23] 23] times*(s(X), @_{o -> o}*(times(s(X)), Y)) >= @_{o -> o}(plus(@_{o -> o}(times(X), Y)), Y) because times > @_{o -> o}, [24] and [33], by (Copy) 24] times*(s(X), @_{o -> o}*(times(s(X)), Y)) >= plus(@_{o -> o}(times(X), Y)) because times > plus and [25], by (Copy) 25] times*(s(X), @_{o -> o}*(times(s(X)), Y)) >= @_{o -> o}(times(X), Y) because [26], by (Select) 26] @_{o -> o}*(times(s(X)), Y) >= @_{o -> o}(times(X), Y) because @_{o -> o} in Mul, [27] and [32], by (Stat)
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