details

property	value
status	complete
benchmark	Ex6_9_Luc02c_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0571439266205 seconds
cpu usage	0.041094316
max memory	2551808.0

stage attributes

key	value
output-size	2361
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. 2nd : [o] --> o activate : [o] --> o cons : [o * o] --> o cons1 : [o * o] --> o from : [o] --> o n!6220!6220from : [o] --> o s : [o] --> o 2nd(cons1(X, cons(Y, Z))) => Y 2nd(cons(X, Y)) => 2nd(cons1(X, activate(Y))) from(X) => cons(X, n!6220!6220from(s(X))) from(X) => n!6220!6220from(X) activate(n!6220!6220from(X)) => from(X) activate(X) => X 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] 2nd#(cons(X, Y)) =#> 2nd#(cons1(X, activate(Y))) 1] 2nd#(cons(X, Y)) =#> activate#(Y) 2] activate#(n!6220!6220from(X)) =#> from#(X) Rules R_0: 2nd(cons1(X, cons(Y, Z))) => Y 2nd(cons(X, Y)) => 2nd(cons1(X, activate(Y))) from(X) => cons(X, n!6220!6220from(s(X))) from(X) => n!6220!6220from(X) activate(n!6220!6220from(X)) => from(X) activate(X) => X 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 : 2 * 2 : 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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