details

property	value
status	complete
benchmark	4.18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0827760696411 seconds
cpu usage	0.051250487
max memory	3416064.0

stage attributes

key	value
output-size	2068
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. !770 : [o * o] --> o !minus : [o * o] --> o 0 : [] --> o gcd : [o * o] --> o if : [o * o * o] --> o s : [o] --> o gcd(X, 0) => X gcd(0, X) => X gcd(s(X), s(Y)) => if(!770(X, Y), gcd(s(X), !minus(Y, X)), gcd(!minus(X, Y), s(Y))) We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]). We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] gcd#(s(X), s(Y)) =#> gcd#(s(X), !minus(Y, X)) 1] gcd#(s(X), s(Y)) =#> gcd#(!minus(X, Y), s(Y)) Rules R_0: gcd(X, 0) => X gcd(0, X) => X gcd(s(X), s(Y)) => if(!770(X, Y), gcd(s(X), !minus(Y, X)), gcd(!minus(X, Y), s(Y))) Thus, the original system is terminating if (P_0, R_0, minimal, formative) is finite. We consider the dependency pair problem (P_0, R_0, minimal, formative). We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows: * 0 : * 1 : This graph has no strongly connected components. By [Kop12, Thm. 7.31], this implies finiteness of the dependency pair problem. As all dependency pair problems were succesfully simplified with sound (and complete) processors until nothing remained, we conclude termination. +++ Citations +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. [KusIsoSakBla09] K. Kusakari, Y. Isogai, M. Sakai, and F. Blanqui. Static Dependency Pair Method Based On Strong Computability for Higher-Order Rewrite Systems. In volume 92(10) of IEICE Transactions on Information and Systems. 2007--2015, 2009. popout

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