details

property	value
status	complete
benchmark	otto04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n094.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	1.45327281952 seconds
cpu usage	1.444038251
max memory	3.3255424E7

stage attributes

key	value
output-size	1882
starexec-result	MAYBE

output

/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o false : [] --> o fib : [o] --> o fibo : [o] --> o if : [o * o * o * o * o] --> o lt : [o * o] --> o s : [o] --> o sum : [o * o] --> o true : [] --> o lt(0, s(X)) => true lt(X, 0) => false lt(s(X), s(Y)) => lt(X, Y) fibo(0) => fib(0) fibo(s(0)) => fib(s(0)) fibo(s(s(X))) => sum(fibo(s(X)), fibo(X)) fib(0) => s(0) fib(s(0)) => s(0) fib(s(s(X))) => if(true, 0, s(s(X)), 0, 0) if(true, X, s(s(Y)), Z, U) => if(lt(s(X), s(s(Y))), s(X), s(s(Y)), U, X) if(false, X, s(s(Y)), Z, U) => sum(fibo(Z), fibo(U)) sum(X, 0) => X sum(X, s(Y)) => s(sum(X, Y)) As the system is orthogonal, it is terminating if it is innermost terminating by [Gra95]. Then, by [FuhGieParSchSwi11], it suffices to prove (innermost) termination of the typed system, with sort annotations chosen to respect the rules, as follows: 0 : [] --> ne false : [] --> dd fib : [ne] --> ne fibo : [ne] --> ne if : [dd * ne * ne * ne * ne] --> ne lt : [ne * ne] --> dd s : [ne] --> ne sum : [ne * ne] --> ne true : [] --> dd +++ Citations +++ [FuhGieParSchSwi11] C. Fuhs, J. Giesl, M. Parting, P. Schneider-Kamp, and S. Swiderski. Proving Termination by Dependency Pairs and Inductive Theorem Proving. In volume 47(2) of Journal of Automated Reasoning. 133--160, 2011. [Gra95] B. Gramlich. Abstract Relations Between Restricted Termination and Confluence Properties of Rewrite Systems. In volume 24(1-2) of Fundamentae Informaticae. 3--23, 1995. popout

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actions

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