details

property	value
status	complete
benchmark	4.51.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n058.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0815348625183 seconds
cpu usage	0.067014782
max memory	2187264.0

stage attributes

key	value
output-size	3956
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. a : [] --> o f : [o] --> o g : [o] --> o h : [o] --> o k : [o * o * o] --> o f(a) => g(h(a)) h(g(X)) => g(h(f(X))) k(X, h(X), a) => h(X) k(f(X), Y, X) => f(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]): f(a) >? g(h(a)) h(g(X)) >? g(h(f(X))) k(X, h(X), a) >? h(X) k(f(X), Y, X) >? f(X) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: a = 0 f = \y0.y0 g = \y0.y0 h = \y0.y0 k = \y0y1y2.3 + 3y0 + 3y1 + 3y2 Using this interpretation, the requirements translate to: [[f(a)]] = 0 >= 0 = [[g(h(a))]] [[h(g(_x0))]] = x0 >= x0 = [[g(h(f(_x0)))]] [[k(_x0, h(_x0), a)]] = 3 + 6x0 > x0 = [[h(_x0)]] [[k(f(_x0), _x1, _x0)]] = 3 + 3x1 + 6x0 > x0 = [[f(_x0)]] We can thus remove the following rules: k(X, h(X), a) => h(X) k(f(X), Y, X) => f(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]). We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] f#(a) =#> h#(a) 1] h#(g(X)) =#> h#(f(X)) 2] h#(g(X)) =#> f#(X) Rules R_0: f(a) => g(h(a)) h(g(X)) => g(h(f(X))) Thus, the original system is terminating if (P_0, R_0, minimal, formative) is finite. We consider the dependency pair problem (P_0, R_0, minimal, formative). We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows: * 0 : * 1 : 1, 2 * 2 : 0 This graph has the following strongly connected components: P_1: h#(g(X)) =#> h#(f(X)) By [Kop12, Thm. 7.31], we may replace any dependency pair problem (P_0, R_0, m, f) by (P_1, R_0, m, f). Thus, the original system is terminating if (P_1, R_0, minimal, formative) is finite. We consider the dependency pair problem (P_1, R_0, minimal, formative). We will use the reduction pair processor [Kop12, Thm. 7.16]. It suffices to find a standard reduction pair [Kop12, Def. 6.69]. Thus, we must orient: h#(g(X)) >? h#(f(X)) f(a) >= g(h(a)) h(g(X)) >= g(h(f(X))) We orient these requirements with a polynomial interpretation in the natural numbers. We consider usable_rules with respect to the following argument filtering: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Stand 20472