details

property	value
status	complete
benchmark	kop12thesis_sec3.3.3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Kop_13

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.053406 seconds
cpu usage	0.053455
user time	0.043975
system time	0.00948
max virtual memory	113188.0
max residence set size	2820.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: f : [o -> o] --> o g : [] --> o -> o Rules: f(g) => f(/\x.g x) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We use the dependency pair framework as described in [Kop12, Ch. 6/7], with dynamic dependency pairs. We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] f#(g) =#> f#(/\x.g x) Rules R_0: f(g) => f(/\x.g 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 : 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. popout

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all output return to Higher Order Rewriting Union Beta