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HRS union beta 16688 pair #381734466
details
property
value
status
complete
benchmark
AotoYamada_05__020.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.0905680656433 seconds
cpu usage
0.086338042
max memory
4960256.0
stage attributes
key
value
output-size
5188
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: 0 : [] --> a comp : [b -> b * b -> b] --> b -> b plus : [a * a] --> a s : [a] --> a times : [a * a] --> a twice : [b -> 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) comp(f, g) x => f (g x) twice(f) => comp(f, f) 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) comp(F, G) X >? F (G X) twice(F) >? comp(F, F) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[0]] = _|_ We choose Lex = {} and Mul = {@_{o -> o}, comp, plus, s, times, twice}, and the following precedence: times > plus > s > twice > comp > @_{o -> o} Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: plus(_|_, X) >= X plus(s(X), Y) >= s(plus(X, Y)) times(_|_, X) >= _|_ times(s(X), Y) > plus(times(X, Y), Y) @_{o -> o}(comp(F, G), X) > @_{o -> o}(F, @_{o -> o}(G, X)) twice(F) >= comp(F, F) With these choices, we have: 1] plus(_|_, X) >= X because [2], by (Star) 2] plus*(_|_, X) >= X because [3], by (Select) 3] X >= X by (Meta) 4] plus(s(X), Y) >= s(plus(X, Y)) because [5], by (Star) 5] plus*(s(X), Y) >= s(plus(X, Y)) because plus > s and [6], by (Copy) 6] plus*(s(X), Y) >= plus(X, Y) because plus in Mul, [7] and [10], by (Stat) 7] s(X) > X because [8], by definition 8] s*(X) >= X because [9], by (Select) 9] X >= X by (Meta) 10] Y >= Y by (Meta) 11] times(_|_, X) >= _|_ by (Bot) 12] times(s(X), Y) > plus(times(X, Y), Y) because [13], by definition 13] times*(s(X), Y) >= plus(times(X, Y), Y) because times > plus, [14] and [19], by (Copy) 14] times*(s(X), Y) >= times(X, Y) because times in Mul, [15] and [18], by (Stat) 15] s(X) > X because [16], by definition 16] s*(X) >= X because [17], by (Select) 17] X >= X by (Meta) 18] Y >= Y by (Meta) 19] times*(s(X), Y) >= Y because [18], by (Select) 20] @_{o -> o}(comp(F, G), X) > @_{o -> o}(F, @_{o -> o}(G, X)) because [21], by definition 21] @_{o -> o}*(comp(F, G), X) >= @_{o -> o}(F, @_{o -> o}(G, X)) because [22], by (Select) 22] comp(F, G) @_{o -> o}*(comp(F, G), X) >= @_{o -> o}(F, @_{o -> o}(G, X)) because [23] 23] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= @_{o -> o}(F, @_{o -> o}(G, X)) because comp > @_{o -> o}, [24] and [26], by (Copy) 24] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= F because [25], by (Select) 25] F >= F by (Meta) 26] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= @_{o -> o}(G, X) because comp > @_{o -> o}, [27] and [29], by (Copy) 27] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= G because [28], by (Select) 28] G >= G by (Meta) 29] comp*(F, G, @_{o -> o}*(comp(F, G), X)) >= X because [30], by (Select) 30] @_{o -> o}*(comp(F, G), X) >= X because [31], by (Select) 31] X >= X by (Meta) 32] twice(F) >= comp(F, F) because [33], by (Star) 33] twice*(F) >= comp(F, F) because twice > comp, [34] and [34], by (Copy) 34] twice*(F) >= F because [35], by (Select)
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