details

property	value
status	complete
benchmark	03minus.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	Blanqui_15

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.0170259475708 seconds
cpu usage	0.014308331
max memory	1069056.0

stage attributes

key	value
output-size	1687
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: minus : [N * N] --> N s : [N] --> N z : [] --> N Rules: minus(z, x) => z minus(x, z) => x minus(s(x), s(y)) => minus(x, y) minus(x, x) => z 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]): minus(z, X) >? z minus(X, z) >? X minus(s(X), s(Y)) >? minus(X, Y) minus(X, X) >? z We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: minus = \y0y1.3 + y1 + 3y0 s = \y0.3 + 3y0 z = 0 Using this interpretation, the requirements translate to: [[minus(z, _x0)]] = 3 + x0 > 0 = [[z]] [[minus(_x0, z)]] = 3 + 3x0 > x0 = [[_x0]] [[minus(s(_x0), s(_x1))]] = 15 + 3x1 + 9x0 > 3 + x1 + 3x0 = [[minus(_x0, _x1)]] [[minus(_x0, _x0)]] = 3 + 4x0 > 0 = [[z]] We can thus remove the following rules: minus(z, X) => z minus(X, z) => X minus(s(X), s(Y)) => minus(X, Y) minus(X, X) => z 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

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actions

all output return to HRS union beta 16688