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	n149.star.cs.uiowa.edu
space	Hamana_17

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.126471 seconds
cpu usage	0.122999
user time	0.095519
system time	0.02748
max virtual memory	113188.0
max residence set size	4808.0

stage attributes

key	value
starexec-result	YES

output

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 Symbols ~AP1, ~AP2, and ~AP3 are encodings for application that are only used in innocuous ways. We can simplify the program (without losing non-termination) by removing them. Additionally, we can remove some (now-)redundant rules. This gives: 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.X(x)), Y) => X(Y) 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.Y(x), /\y.Z(y)) => Y(X) case(inr(X), /\x.Y(x), /\y.Z(y)) => Z(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: || Input TRS: || 1: piA(pair(PeRCenTX,PeRCenTY)) -> PeRCenTX || 2: piB(pair(PeRCenTX,PeRCenTY)) -> PeRCenTY || 3: pair(piA(PeRCenTX),piB(PeRCenTX)) -> PeRCenTX || 4: TIlDePAIR(PeRCenTX,PeRCenTY) -> PeRCenTX || 5: TIlDePAIR(PeRCenTX,PeRCenTY) -> PeRCenTY || Number of strict rules: 5 || Direct POLO(bPol) ... removes: 4 1 3 5 2 || piB w: 2 * x1 + 1 popout

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

job log

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actions

all output return to Higher Order Rewriting Union Beta