details

property	value
status	complete
benchmark	DicosmoKesner93.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n097.star.cs.uiowa.edu
space	Hamana_17

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.893044948578 seconds
cpu usage	1.576044351
max memory	7.7615104E7

stage attributes

key	value
output-size	6894
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: app : [] --> arrAB -> A -> B case : [] --> SAB -> A -> C -> B -> C -> C inl : [] --> A -> SAB inr : [] --> B -> SAB lam : [] --> A -> B -> arrAB pair : [] --> A -> B -> PAB piA : [] --> PAB -> A piB : [] --> PAB -> B Rules: app (lam (/\x.f x)) y => f y lam (/\x.app y x) => y piA (pair x y) => x piB (pair x y) => y pair (piA x) (piB x) => x case (inl x) (/\y.f y) (/\z.g z) => f x case (inr x) (/\y.f y) (/\z.g z) => g x Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term. We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0). This leads to the following AFSM: Alphabet: app : [arrAB * A] --> B case : [SAB * A -> C * B -> C] --> C inl : [A] --> SAB inr : [B] --> SAB lam : [A -> B] --> arrAB pair : [A * B] --> PAB piA : [PAB] --> A piB : [PAB] --> B ~AP1 : [A -> B * A] --> B ~AP2 : [A -> C * A] --> C ~AP3 : [B -> C * B] --> C Rules: app(lam(/\x.~AP1(F, x)), X) => ~AP1(F, X) lam(/\x.app(X, x)) => X piA(pair(X, Y)) => X piB(pair(X, Y)) => Y pair(piA(X), piB(X)) => X case(inl(X), /\x.~AP2(F, x), /\y.~AP3(G, y)) => ~AP2(F, X) case(inr(X), /\x.~AP2(F, x), /\y.~AP3(G, y)) => ~AP3(G, X) app(lam(/\x.app(X, x)), Y) => app(X, Y) ~AP1(F, X) => F X ~AP2(F, X) => F X ~AP3(F, X) => F X We observe that the rules contain a first-order subset: piA(pair(X, Y)) => X piB(pair(X, Y)) => Y pair(piA(X), piB(X)) => X Moreover, the system is finitely branching. 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 Ce-terminating when seen as a many-sorted first-order TRS. According to the external first-order termination prover, this system is indeed Ce-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) QTRSRRRProof [EQUIVALENT] || (2) QTRS || (3) RisEmptyProof [EQUIVALENT] || (4) YES || || || ---------------------------------------- || || (0) || Obligation: || Q restricted rewrite system: || The TRS R consists of the following rules: || || piA(pair(%X, %Y)) -> %X || piB(pair(%X, %Y)) -> %Y || pair(piA(%X), piB(%X)) -> %X || ~PAIR(%X, %Y) -> %X || ~PAIR(%X, %Y) -> %Y || || Q is empty. || popout

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

job log

popout

actions

all output return to HRS union beta 16688