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HRS union beta 16688 pair #381734475
details
property
value
status
complete
benchmark
AotoYamada_05__021.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.589569091797 seconds
cpu usage
0.58618457
max memory
2.4461312E7
stage attributes
key
value
output-size
21109
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 : [] --> a cons : [a * b] --> b double : [b] --> b inc : [b] --> b map : [a -> a * b] --> b nil : [] --> b plus : [a] --> a -> a s : [a] --> a times : [a] --> a -> a 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 inc(x) => map(plus(s(0)), x) double(x) => map(times(s(s(0))), x) map(f, nil) => nil map(f, cons(x, y)) => cons(f x, map(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]): 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 inc(X) >? map(plus(s(0)), X) double(X) >? map(times(s(s(0))), X) map(F, nil) >? nil map(F, cons(X, Y)) >? cons(F X, map(F, Y)) 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 > cons > times > @_{o -> o} > s > plus 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) inc(X) >= map(plus(s(_|_)), X) double(X) >= map(times(s(s(_|_))), X) map(F, _|_) > _|_ map(F, cons(X, Y)) >= cons(@_{o -> o}(F, X), map(F, Y)) 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 (Star) 5] @_{o -> o}*(plus(s(X)), Y) >= s(@_{o -> o}(plus(X), Y)) because @_{o -> o} > s and [6], by (Copy) 6] @_{o -> o}*(plus(s(X)), Y) >= @_{o -> o}(plus(X), Y) because @_{o -> o} in Mul, [7] and [12], by (Stat) 7] plus(s(X)) > plus(X) because [8], by definition 8] plus*(s(X)) >= plus(X) because plus in Mul and [9], by (Stat) 9] s(X) > X because [10], by definition 10] s*(X) >= X because [11], by (Select) 11] X >= X by (Meta) 12] Y >= Y by (Meta) 13] @_{o -> o}(times(_|_), X) >= _|_ by (Bot) 14] @_{o -> o}(times(s(X)), Y) >= @_{o -> o}(plus(@_{o -> o}(times(X), Y)), Y) because [15], by (Star) 15] @_{o -> o}*(times(s(X)), Y) >= @_{o -> o}(plus(@_{o -> o}(times(X), Y)), Y) because [16], by (Select) 16] times(s(X)) @_{o -> o}*(times(s(X)), Y) >= @_{o -> o}(plus(@_{o -> o}(times(X), Y)), Y) because [17] 17] times*(s(X), @_{o -> o}*(times(s(X)), Y)) >= @_{o -> o}(plus(@_{o -> o}(times(X), Y)), Y) because times > @_{o -> o}, [18] and [24], by (Copy) 18] times*(s(X), @_{o -> o}*(times(s(X)), Y)) >= plus(@_{o -> o}(times(X), Y)) because times > plus and [19], by (Copy) 19] times*(s(X), @_{o -> o}*(times(s(X)), Y)) >= @_{o -> o}(times(X), Y) because times > @_{o -> o}, [20] and [24], by (Copy) 20] times*(s(X), @_{o -> o}*(times(s(X)), Y)) >= times(X) because times in Mul and [21], by (Stat) 21] s(X) > X because [22], by definition 22] s*(X) >= X because [23], by (Select) 23] X >= X by (Meta) 24] times*(s(X), @_{o -> o}*(times(s(X)), Y)) >= Y because [25], by (Select) 25] @_{o -> o}*(times(s(X)), Y) >= Y because [26], by (Select) 26] Y >= Y by (Meta)
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