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Higher Order Rewriting Union Beta pair #487093881
details
property
value
status
complete
benchmark
04arrow.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Blanqui_15
run statistics
property
value
solver
Wanda 2.2a
configuration
default
runtime (wallclock)
0.0186791 seconds
cpu usage
0.018686
user time
0.01227
system time
0.006416
max virtual memory
113188.0
max residence set size
1724.0
stage attributes
key
value
starexec-result
YES
output
YES We consider the system theBenchmark. Alphabet: and : [c * c] --> c arrow : [t * t] --> t lessthan : [t * t] --> c Rules: lessthan(arrow(x, y), arrow(z, u)) => and(lessthan(z, x), lessthan(y, u)) 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]): lessthan(arrow(X, Y), arrow(Z, U)) >? and(lessthan(Z, X), lessthan(Y, U)) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: and = \y0y1.y0 + y1 arrow = \y0y1.3 + 3y0 + 3y1 lessthan = \y0y1.2y0 + 3y1 Using this interpretation, the requirements translate to: [[lessthan(arrow(_x0, _x1), arrow(_x2, _x3))]] = 15 + 6x0 + 6x1 + 9x2 + 9x3 > 2x1 + 2x2 + 3x0 + 3x3 = [[and(lessthan(_x2, _x0), lessthan(_x1, _x3))]] We can thus remove the following rules: lessthan(arrow(X, Y), arrow(Z, U)) => and(lessthan(Z, X), lessthan(Y, U)) 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.
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