details

property	value
status	complete
benchmark	Applicative_05__mapDivMinusHard.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n109.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.885381937027 seconds
cpu usage	1.925948635
max memory	1.25874176E8

stage attributes

key	value
output-size	13389
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: 0 : [] --> c cons : [a * b] --> b div : [c * c] --> c map : [a -> a * b] --> b minus : [c * c] --> c nil : [] --> b p : [c] --> c s : [c] --> c Rules: map(f, nil) => nil map(f, cons(x, y)) => cons(f x, map(f, y)) minus(x, 0) => x minus(s(x), s(y)) => minus(p(s(x)), p(s(y))) p(s(x)) => x div(0, s(x)) => 0 div(s(x), s(y)) => s(div(minus(x, y), s(y))) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We observe that the rules contain a first-order subset: minus(X, 0) => X minus(s(X), s(Y)) => minus(p(s(X)), p(s(Y))) p(s(X)) => X div(0, s(X)) => 0 div(s(X), s(Y)) => s(div(minus(X, Y), s(Y))) Moreover, the system is orthogonal. Thus, by [Kop12, Thm. 7.55], we may omit all first-order dependency pairs from the dependency pair problem (DP(R), R) if this first-order part is terminating when seen as a many-sorted first-order TRS. According to the external first-order termination prover, this system is indeed terminating: || proof of resources/system.trs || # AProVE Commit ID: d84c10301d352dfd14de2104819581f4682260f5 fuhs 20130616 || || || Termination w.r.t. Q of the given QTRS could be proven: || || (0) QTRS || (1) Overlay + Local Confluence [EQUIVALENT] || (2) QTRS || (3) DependencyPairsProof [EQUIVALENT] || (4) QDP || (5) DependencyGraphProof [EQUIVALENT] || (6) AND || (7) QDP || (8) UsableRulesProof [EQUIVALENT] || (9) QDP || (10) QReductionProof [EQUIVALENT] || (11) QDP || (12) MRRProof [EQUIVALENT] || (13) QDP || (14) DependencyGraphProof [EQUIVALENT] || (15) TRUE || (16) QDP || (17) UsableRulesProof [EQUIVALENT] || (18) QDP || (19) QReductionProof [EQUIVALENT] || (20) QDP || (21) QDPOrderProof [EQUIVALENT] || (22) QDP || (23) PisEmptyProof [EQUIVALENT] || (24) YES || || || ---------------------------------------- || || (0) || Obligation: || Q restricted rewrite system: || The TRS R consists of the following rules: || || minus(%X, 0) -> %X || minus(s(%X), s(%Y)) -> minus(p(s(%X)), p(s(%Y))) || p(s(%X)) -> %X || div(0, s(%X)) -> 0 || div(s(%X), s(%Y)) -> s(div(minus(%X, %Y), s(%Y))) || || Q is empty. || || ---------------------------------------- || || (1) Overlay + Local Confluence (EQUIVALENT) || The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. || ---------------------------------------- || || (2) || Obligation: popout

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

job log

popout

actions

all output return to HRS union beta 16688