details

property	value
status	complete
benchmark	curry1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Mixed_HO_10

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.0156909 seconds
cpu usage	0.015306
user time	0.00839
system time	0.006916
max virtual memory	0.0
max residence set size	1636.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: f : [] --> a -> b -> c f1 : [a] --> b -> c f2 : [a * b] --> c Rules: f1(x) => f x f2(x, y) => f1(x) y This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): f1(X) >? f(X) f2(X, Y) >? f1(X) Y We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: f = \y0y1.y0 f1 = \y0y1.1 + y0 f2 = \y0y1.3 + 3y0 + 3y1 Using this interpretation, the requirements translate to: [[f1(_x0)]] = \y0.1 + x0 > \y0.x0 = [[f(_x0)]] [[f2(_x0, _x1)]] = 3 + 3x0 + 3x1 > 1 + x0 + x1 = [[f1(_x0) _x1]] We can thus remove the following rules: f1(X) => f(X) f2(X, Y) => f1(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

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Higher Order Rewriting Union Beta