details

property	value
status	complete
benchmark	BTreeMember.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n034.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.44678401947 seconds
cpu usage	0.437492861
max memory	2.0324352E7

stage attributes

key	value
output-size	10592
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. 0 : [] --> o app : [o * o] --> o eq : [] --> o false : [] --> o fork : [] --> o if : [] --> o lt : [] --> o member : [] --> o null : [] --> o s : [] --> o true : [] --> o app(app(lt, app(s, X)), app(s, Y)) => app(app(lt, X), Y) app(app(lt, 0), app(s, X)) => true app(app(lt, X), 0) => false app(app(eq, X), X) => true app(app(eq, app(s, X)), 0) => false app(app(eq, 0), app(s, X)) => false app(app(member, X), null) => false app(app(member, X), app(app(app(fork, Y), Z), U)) => app(app(app(if, app(app(lt, X), Z)), app(app(member, X), Y)), app(app(app(if, app(app(eq, X), Z)), true), app(app(member, X), U))) 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, all): Dependency Pairs P_0: 0] app#(app(lt, app(s, X)), app(s, Y)) =#> app#(app(lt, X), Y) 1] app#(app(lt, app(s, X)), app(s, Y)) =#> app#(lt, X) 2] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(app(if, app(app(lt, X), Z)), app(app(member, X), Y)), app(app(app(if, app(app(eq, X), Z)), true), app(app(member, X), U))) 3] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(if, app(app(lt, X), Z)), app(app(member, X), Y)) 4] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(if, app(app(lt, X), Z)) 5] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(lt, X), Z) 6] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(lt, X) 7] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(member, X), Y) 8] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(member, X) 9] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(app(if, app(app(eq, X), Z)), true), app(app(member, X), U)) 10] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(if, app(app(eq, X), Z)), true) 11] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(if, app(app(eq, X), Z)) 12] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(eq, X), Z) 13] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(eq, X) 14] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(member, X), U) 15] app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(member, X) Rules R_0: app(app(lt, app(s, X)), app(s, Y)) => app(app(lt, X), Y) app(app(lt, 0), app(s, X)) => true app(app(lt, X), 0) => false app(app(eq, X), X) => true app(app(eq, app(s, X)), 0) => false app(app(eq, 0), app(s, X)) => false app(app(member, X), null) => false app(app(member, X), app(app(app(fork, Y), Z), U)) => app(app(app(if, app(app(lt, X), Z)), app(app(member, X), Y)), app(app(app(if, app(app(eq, X), Z)), true), app(app(member, X), U))) Thus, the original system is terminating if (P_0, R_0, minimal, all) is finite. We consider the dependency pair problem (P_0, R_0, minimal, all). We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows: * 0 : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 * 1 : * 2 : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 * 3 : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 * 4 : * 5 : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 * 6 : * 7 : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 * 8 : * 9 : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 * 10 : * 11 : * 12 : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 * 13 : * 14 : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 * 15 : This graph has the following strongly connected components: P_1: app#(app(lt, app(s, X)), app(s, Y)) =#> app#(app(lt, X), Y) app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(app(if, app(app(lt, X), Z)), app(app(member, X), Y)), app(app(app(if, app(app(eq, X), Z)), true), app(app(member, X), U))) app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(if, app(app(lt, X), Z)), app(app(member, X), Y)) app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(lt, X), Z) app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(member, X), Y) app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(app(if, app(app(eq, X), Z)), true), app(app(member, X), U)) app#(app(member, X), app(app(app(fork, Y), Z), U)) =#> app#(app(eq, X), Z) popout

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