details

property	value
status	complete
benchmark	lambda3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Mixed_HO_10

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.042543 seconds
cpu usage	0.037299
user time	0.025195
system time	0.012104
max virtual memory	113188.0
max residence set size	2376.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: fapp : [o * o] --> o h : [o] --> o lam : [o -> o] --> o Rules: fapp(lam(f), x) => f h(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. After applying [Kop12, Thm. 7.22] to denote collapsing dependency pairs in an extended form, we thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] fapp#(lam(F), X) =#> F(h(X)) Rules R_0: fapp(lam(F), X) => F h(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 will use the reduction pair processor [Kop12, Thm. 7.16]. As the system is abstraction-simple and the formative flag is set, it suffices to find a tagged reduction pair [Kop12, Def. 6.70]. Thus, we must orient: fapp#(lam(F), X) >? F(h(X)) fapp(lam(F), X) >= F h(X) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: fapp = \y0y1.3 + 3y0 fapp# = \y0y1.3 + y0 h = \y0.0 lam = \G0.3 + G0(0) Using this interpretation, the requirements translate to: [[fapp#(lam(_F0), _x1)]] = 6 + F0(0) > F0(0) = [[_F0(h(_x1))]] [[fapp(lam(_F0), _x1)]] = 12 + 3F0(0) >= F0(0) = [[_F0 h(_x1)]] By the observations in [Kop12, Sec. 6.6], this reduction pair suffices; we may thus replace a dependency pair problem (P_0, R_0) by ({}, R_0). By the empty set processor [Kop12, Thm. 7.15] this problem may be immediately removed. 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