details

property	value
status	complete
benchmark	map.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n034.star.cs.uiowa.edu
space	Mixed_HO_10

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.0233988761902 seconds
cpu usage	0.018307541
max memory	1499136.0

stage attributes

key	value
output-size	1674
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: cons : [a * list] --> list map : [list * a -> a] --> list nil : [] --> list Rules: map(nil, f) => nil map(cons(x, y), f) => cons(f x, map(y, 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]): map(nil, F) >? nil map(cons(X, Y), F) >? cons(F X, map(Y, F)) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: cons = \y0y1.3 + y0 + y1 map = \y0G1.3 + 3y0 + G1(y0) + 3y0G1(y0) nil = 2 Using this interpretation, the requirements translate to: [[map(nil, _F0)]] = 9 + 7F0(2) > 2 = [[nil]] [[map(cons(_x0, _x1), _F2)]] = 12 + 3x0 + 3x1 + 3x0F2(3 + x0 + x1) + 3x1F2(3 + x0 + x1) + 10F2(3 + x0 + x1) > 6 + x0 + 3x1 + F2(x0) + F2(x1) + 3x1F2(x1) = [[cons(_F2 _x0, map(_x1, _F2))]] We can thus remove the following rules: map(nil, F) => nil map(cons(X, Y), F) => cons(F X, map(Y, F)) All rules were succesfully removed. Thus, termination of the original system has been reduced to termination of the beta-rule, which is well-known to hold. +++ Citations +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. popout

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

job log

popout

actions

all output return to HRS union beta 16688