details

property	value
status	complete
benchmark	AotoYamada_05__023.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n052.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.037801027298 seconds
cpu usage	0.018441398
max memory	1212416.0

stage attributes

key	value
output-size	2042
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: 0 : [] --> a id : [] --> a -> a plus : [a] --> a -> a s : [a] --> a Rules: id x => x plus(0) => id plus(s(x)) y => s(plus(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]): id X >? X plus(0) >? id plus(s(X)) Y >? s(plus(X) Y) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: 0 = 3 id = \y0.3y0 plus = \y0y1.3 + 3y0 + 3y1 s = \y0.3 + y0 Using this interpretation, the requirements translate to: [[id _x0]] = 4x0 >= x0 = [[_x0]] [[plus(0)]] = \y0.12 + 3y0 > \y0.3y0 = [[id]] [[plus(s(_x0)) _x1]] = 12 + 3x0 + 4x1 > 6 + 3x0 + 4x1 = [[s(plus(_x0) _x1)]] We can thus remove the following rules: plus(0) => id plus(s(X)) Y => s(plus(X) Y) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): id(X) >? X We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: id = \y0.1 + y0 Using this interpretation, the requirements translate to: [[id(_x0)]] = 1 + x0 > x0 = [[_x0]] We can thus remove the following rules: id(X) => X 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 HRS union beta 16688