details

property	value
status	complete
benchmark	09ex.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n092.star.cs.uiowa.edu
space	Blanqui_15

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.737787008286 seconds
cpu usage	0.107561227
max memory	6705152.0

stage attributes

key	value
output-size	5443
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: c : [] --> C -> L -> L -> C d : [] --> C ex : [] --> C -> L nil : [] --> L Rules: ex d => nil ex (c (/\f.g f)) => g ex Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term. We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0). This leads to the following AFSM: Alphabet: c : [C -> L -> L] --> C d : [] --> C ex : [] --> C -> L nil : [] --> L ~AP1 : [C -> L -> L * C -> L] --> L Rules: ex d => nil ex c(/\f.~AP1(F, f)) => ~AP1(F, ex) ~AP1(F, G) => F G We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): ex d >? nil ex c(/\f.~AP1(F, f)) >? ~AP1(F, ex) ~AP1(F, G) >? F G about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: [[ex]] = _|_ [[nil]] = _|_ We choose Lex = {} and Mul = {@_{(o -> o) -> o}, @_{o -> o}, c, d, ~AP1}, and the following precedence: d > c > ~AP1 > @_{(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: @_{o -> o}(_|_, d) > _|_ @_{o -> o}(_|_, c(/\f.~AP1(F, f))) >= ~AP1(F, _|_) ~AP1(F, G) >= @_{(o -> o) -> o}(F, G) With these choices, we have: 1] @_{o -> o}(_|_, d) > _|_ because [2], by definition 2] @_{o -> o}*(_|_, d) >= _|_ by (Bot) 3] @_{o -> o}(_|_, c(/\f.~AP1(F, f))) >= ~AP1(F, _|_) because [4], by (Star) 4] @_{o -> o}*(_|_, c(/\f.~AP1(F, f))) >= ~AP1(F, _|_) because [5], by (Select) 5] c(/\f.~AP1(F, f)) >= ~AP1(F, _|_) because [6], by (Star) 6] c*(/\f.~AP1(F, f)) >= ~AP1(F, _|_) because [7], by (Select) 7] ~AP1(F, c*(/\f.~AP1(F, f))) >= ~AP1(F, _|_) because ~AP1 in Mul, [8] and [9], by (Fun) 8] F >= F by (Meta) 9] c*(/\f.~AP1(F, f)) >= _|_ by (Bot) 10] ~AP1(F, G) >= @_{(o -> o) -> o}(F, G) because [11], by (Star) 11] ~AP1*(F, G) >= @_{(o -> o) -> o}(F, G) because ~AP1 > @_{(o -> o) -> o}, [12] and [14], by (Copy) 12] ~AP1*(F, G) >= F because [13], by (Select) 13] F >= F by (Meta) 14] ~AP1*(F, G) >= G because [15], by (Select) 15] G >= G by (Meta) We can thus remove the following rules: ex d => 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]): ex c(/\f.~AP1(F, f)) >? ~AP1(F, ex) ~AP1(F, G) >? F G about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. Argument functions: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to HRS union beta 16688