details

property	value
status	complete
benchmark	Applicative_05__Ex7_9.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n105.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.909981012344 seconds
cpu usage	2.016687798
max memory	8.9829376E7

stage attributes

key	value
output-size	22249
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: 0 : [] --> a cons : [b * c] --> c d : [a * a] --> c false : [] --> c filter : [b -> c * c] --> c gtr : [a * a] --> c if : [c * c * c] --> c len : [c] --> a nil : [] --> c s : [a] --> a sub : [a * a] --> a true : [] --> c Rules: if(true, x, y) => x if(false, x, y) => y sub(x, 0) => x sub(s(x), s(y)) => sub(x, y) gtr(0, x) => false gtr(s(x), 0) => true gtr(s(x), s(y)) => gtr(x, y) d(x, 0) => true d(s(x), s(y)) => if(gtr(x, y), false, d(s(x), sub(y, x))) len(nil) => 0 len(cons(x, y)) => s(len(y)) filter(f, nil) => nil filter(f, cons(x, y)) => if(f x, cons(x, filter(f, y)), filter(f, 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: if(true, X, Y) => X if(false, X, Y) => Y sub(X, 0) => X sub(s(X), s(Y)) => sub(X, Y) gtr(0, X) => false gtr(s(X), 0) => true gtr(s(X), s(Y)) => gtr(X, Y) d(X, 0) => true d(s(X), s(Y)) => if(gtr(X, Y), false, d(s(X), sub(Y, X))) len(nil) => 0 len(cons(X, Y)) => s(len(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) QDPSizeChangeProof [EQUIVALENT] || (13) YES || (14) QDP || (15) UsableRulesProof [EQUIVALENT] || (16) QDP || (17) QReductionProof [EQUIVALENT] || (18) QDP || (19) QDPSizeChangeProof [EQUIVALENT] || (20) YES || (21) QDP || (22) UsableRulesProof [EQUIVALENT] || (23) QDP || (24) QReductionProof [EQUIVALENT] || (25) QDP || (26) QDPSizeChangeProof [EQUIVALENT] || (27) YES || (28) QDP || (29) UsableRulesProof [EQUIVALENT] || (30) QDP || (31) QReductionProof [EQUIVALENT] || (32) QDP || (33) QDPOrderProof [EQUIVALENT] popout

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actions

all output return to HRS union beta 16688