Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Higher Order Rewriting Union Beta pair #487093875
details
property
value
status
complete
benchmark
uncurry.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Mixed_HO_10
run statistics
property
value
solver
Wanda 2.2a
configuration
default
runtime (wallclock)
0.0334501 seconds
cpu usage
0.022536
user time
0.012856
system time
0.00968
max virtual memory
113188.0
max residence set size
1692.0
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: f x => f1(x) f1(x) y => f2(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]): f(X) >? f1(X) f1(X) Y >? f2(X, Y) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: f = \y0y1.3 + 3y0 + 3y1 f1 = \y0y1.y0 f2 = \y0y1.y0 + y1 Using this interpretation, the requirements translate to: [[f(_x0)]] = \y0.3 + 3y0 + 3x0 > \y0.x0 = [[f1(_x0)]] [[f1(_x0) _x1]] = x0 + x1 >= x0 + x1 = [[f2(_x0, _x1)]] We can thus remove the following rules: f(X) => f1(X) 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, Y) >? f2(X, Y) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: f1 = \y0y1.3 + 3y0 + 3y1 f2 = \y0y1.y0 + y1 Using this interpretation, the requirements translate to: [[f1(_x0, _x1)]] = 3 + 3x0 + 3x1 > x0 + x1 = [[f2(_x0, _x1)]] We can thus remove the following rules: f1(X, Y) => f2(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
popout
actions
all output
return to Higher Order Rewriting Union Beta