details

property	value
status	complete
benchmark	Ex25_Luc06_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n088.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.216895103455 seconds
cpu usage	0.204695229
max memory	6164480.0

stage attributes

key	value
output-size	10985
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. active : [o] --> o c : [o] --> o d : [o] --> o f : [o] --> o g : [o] --> o h : [o] --> o mark : [o] --> o active(f(f(X))) => mark(c(f(g(f(X))))) active(c(X)) => mark(d(X)) active(h(X)) => mark(c(d(X))) mark(f(X)) => active(f(mark(X))) mark(c(X)) => active(c(X)) mark(g(X)) => active(g(X)) mark(d(X)) => active(d(X)) mark(h(X)) => active(h(mark(X))) f(mark(X)) => f(X) f(active(X)) => f(X) c(mark(X)) => c(X) c(active(X)) => c(X) g(mark(X)) => g(X) g(active(X)) => g(X) d(mark(X)) => d(X) d(active(X)) => d(X) h(mark(X)) => h(X) h(active(X)) => h(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]): active(f(f(X))) >? mark(c(f(g(f(X))))) active(c(X)) >? mark(d(X)) active(h(X)) >? mark(c(d(X))) mark(f(X)) >? active(f(mark(X))) mark(c(X)) >? active(c(X)) mark(g(X)) >? active(g(X)) mark(d(X)) >? active(d(X)) mark(h(X)) >? active(h(mark(X))) f(mark(X)) >? f(X) f(active(X)) >? f(X) c(mark(X)) >? c(X) c(active(X)) >? c(X) g(mark(X)) >? g(X) g(active(X)) >? g(X) d(mark(X)) >? d(X) d(active(X)) >? d(X) h(mark(X)) >? h(X) h(active(X)) >? h(X) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: active = \y0.y0 c = \y0.y0 d = \y0.y0 f = \y0.y0 g = \y0.y0 h = \y0.1 + y0 mark = \y0.y0 Using this interpretation, the requirements translate to: [[active(f(f(_x0)))]] = x0 >= x0 = [[mark(c(f(g(f(_x0)))))]] [[active(c(_x0))]] = x0 >= x0 = [[mark(d(_x0))]] [[active(h(_x0))]] = 1 + x0 > x0 = [[mark(c(d(_x0)))]] [[mark(f(_x0))]] = x0 >= x0 = [[active(f(mark(_x0)))]] [[mark(c(_x0))]] = x0 >= x0 = [[active(c(_x0))]] [[mark(g(_x0))]] = x0 >= x0 = [[active(g(_x0))]] [[mark(d(_x0))]] = x0 >= x0 = [[active(d(_x0))]] [[mark(h(_x0))]] = 1 + x0 >= 1 + x0 = [[active(h(mark(_x0)))]] [[f(mark(_x0))]] = x0 >= x0 = [[f(_x0)]] [[f(active(_x0))]] = x0 >= x0 = [[f(_x0)]] [[c(mark(_x0))]] = x0 >= x0 = [[c(_x0)]] [[c(active(_x0))]] = x0 >= x0 = [[c(_x0)]] [[g(mark(_x0))]] = x0 >= x0 = [[g(_x0)]] [[g(active(_x0))]] = x0 >= x0 = [[g(_x0)]] [[d(mark(_x0))]] = x0 >= x0 = [[d(_x0)]] [[d(active(_x0))]] = x0 >= x0 = [[d(_x0)]] [[h(mark(_x0))]] = 1 + x0 >= 1 + x0 = [[h(_x0)]] [[h(active(_x0))]] = 1 + x0 >= 1 + x0 = [[h(_x0)]] We can thus remove the following rules: active(h(X)) => mark(c(d(X))) We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]). popout

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