Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
HRS union beta 16688 pair #381734556
details
property
value
status
complete
benchmark
AotoYamada_05__Ex5TermProof.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.283272027969 seconds
cpu usage
0.279845862
max memory
1.5765504E7
stage attributes
key
value
output-size
9535
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 add : [a * a] --> a fact : [] --> a -> a mult : [] --> a -> a -> a rec : [a -> a -> a * a] --> a -> a s : [a] --> a Rules: add(0, x) => x add(s(x), y) => s(add(x, y)) mult 0 x => 0 mult s(x) y => add(mult x y, y) rec(f, x) 0 => x rec(f, x) s(y) => f s(y) (rec(f, x) y) fact => rec(mult, 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]): add(0, X) >? X add(s(X), Y) >? s(add(X, Y)) mult 0 X >? 0 mult s(X) Y >? add(mult X Y, Y) rec(F, X) 0 >? X rec(F, X) s(Y) >? F s(Y) (rec(F, X) Y) fact >? rec(mult, s(0)) 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 -> o}, @_{o -> o}, add, fact, mult, rec, s}, and the following precedence: fact > mult > add > s > rec > @_{o -> o -> o} > @_{o -> o} Taking the argument function into account, and fixing the greater / greater equal choices, the constraints can be denoted as follows: add(_|_, X) >= X add(s(X), Y) > s(add(X, Y)) @_{o -> o}(@_{o -> o -> o}(mult, _|_), X) >= _|_ @_{o -> o}(@_{o -> o -> o}(mult, s(X)), Y) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) @_{o -> o}(rec(F, X), _|_) > X @_{o -> o}(rec(F, X), s(Y)) > @_{o -> o}(@_{o -> o -> o}(F, s(Y)), @_{o -> o}(rec(F, X), Y)) fact > rec(mult, s(_|_)) With these choices, we have: 1] add(_|_, X) >= X because [2], by (Star) 2] add*(_|_, X) >= X because [3], by (Select) 3] X >= X by (Meta) 4] add(s(X), Y) > s(add(X, Y)) because [5], by definition 5] add*(s(X), Y) >= s(add(X, Y)) because add > s and [6], by (Copy) 6] add*(s(X), Y) >= add(X, Y) because add 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] @_{o -> o}(@_{o -> o -> o}(mult, _|_), X) >= _|_ by (Bot) 12] @_{o -> o}(@_{o -> o -> o}(mult, s(X)), Y) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) because [13], by (Star) 13] @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) because [14], by (Select) 14] @_{o -> o -> o}(mult, s(X)) @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) because [15] 15] @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) because [16], by (Select) 16] @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) because [17], by (Select) 17] @_{o -> o -> o}(mult, s(X)) @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) because [18] 18] @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) because [19], by (Select) 19] mult @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)) @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) because [20] 20] mult*(@_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)), @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y))) >= add(@_{o -> o}(@_{o -> o -> o}(mult, X), Y), Y) because mult > add, [21] and [31], by (Copy) 21] mult*(@_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)), @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y))) >= @_{o -> o}(@_{o -> o -> o}(mult, X), Y) because [22], by (Select) 22] @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)) >= @_{o -> o}(@_{o -> o -> o}(mult, X), Y) because @_{o -> o -> o} > @_{o -> o}, [23] and [28], by (Copy) 23] @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)) >= @_{o -> o -> o}(mult, X) because @_{o -> o -> o} in Mul, [24] and [25], by (Stat) 24] mult >= mult by (Fun) 25] s(X) > X because [26], by definition 26] s*(X) >= X because [27], by (Select) 27] X >= X by (Meta) 28] @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)) >= Y because [29], by (Select) 29] @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y) >= Y because [30], by (Select) 30] Y >= Y by (Meta) 31] mult*(@_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y)), @_{o -> o -> o}*(mult, s(X), @_{o -> o}*(@_{o -> o -> o}(mult, s(X)), Y))) >= Y because [28], by (Select) 32] @_{o -> o}(rec(F, X), _|_) > X because [33], by definition
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to HRS union beta 16688