details

property	value
status	complete
benchmark	01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n042.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0279350280762 seconds
cpu usage	0.024244725
max memory	1302528.0

stage attributes

key	value
output-size	2690
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. !3220 : [o * o] --> o !div : [o * o] --> o !dot : [o * o] --> o e : [] --> o !3220(X, X) => e !div(X, X) => e !dot(e, X) => X !dot(X, e) => X !3220(e, X) => X !div(X, e) => X !dot(X, !3220(X, Y)) => Y !dot(!div(X, Y), Y) => X !3220(X, !dot(X, Y)) => Y !div(!dot(X, Y), Y) => X !div(X, !3220(Y, X)) => Y !3220(!div(X, Y), X) => Y We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): !3220(X, X) >? e !div(X, X) >? e !dot(e, X) >? X !dot(X, e) >? X !3220(e, X) >? X !div(X, e) >? X !dot(X, !3220(X, Y)) >? Y !dot(!div(X, Y), Y) >? X !3220(X, !dot(X, Y)) >? Y !div(!dot(X, Y), Y) >? X !div(X, !3220(Y, X)) >? Y !3220(!div(X, Y), X) >? Y We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: !3220 = \y0y1.3 + y0 + y1 !div = \y0y1.3 + y0 + y1 !dot = \y0y1.3 + y0 + y1 e = 0 Using this interpretation, the requirements translate to: [[!3220(_x0, _x0)]] = 3 + 2x0 > 0 = [[e]] [[!div(_x0, _x0)]] = 3 + 2x0 > 0 = [[e]] [[!dot(e, _x0)]] = 3 + x0 > x0 = [[_x0]] [[!dot(_x0, e)]] = 3 + x0 > x0 = [[_x0]] [[!3220(e, _x0)]] = 3 + x0 > x0 = [[_x0]] [[!div(_x0, e)]] = 3 + x0 > x0 = [[_x0]] [[!dot(_x0, !3220(_x0, _x1))]] = 6 + x1 + 2x0 > x1 = [[_x1]] [[!dot(!div(_x0, _x1), _x1)]] = 6 + x0 + 2x1 > x0 = [[_x0]] [[!3220(_x0, !dot(_x0, _x1))]] = 6 + x1 + 2x0 > x1 = [[_x1]] [[!div(!dot(_x0, _x1), _x1)]] = 6 + x0 + 2x1 > x0 = [[_x0]] [[!div(_x0, !3220(_x1, _x0))]] = 6 + x1 + 2x0 > x1 = [[_x1]] [[!3220(!div(_x0, _x1), _x0)]] = 6 + x1 + 2x0 > x1 = [[_x1]] We can thus remove the following rules: !3220(X, X) => e !div(X, X) => e !dot(e, X) => X !dot(X, e) => X !3220(e, X) => X !div(X, e) => X !dot(X, !3220(X, Y)) => Y !dot(!div(X, Y), Y) => X !3220(X, !dot(X, Y)) => Y !div(!dot(X, Y), Y) => X !div(X, !3220(Y, X)) => Y !3220(!div(X, Y), X) => Y 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

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