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Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270373
details
property
value
status
complete
benchmark
h05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n156.star.cs.uiowa.edu
space
Hamana_Kikuchi_18
run statistics
property
value
solver
Wanda 2.1c
configuration
default
runtime (wallclock)
124.135 seconds
cpu usage
124.861
user time
110.356
system time
14.5051
max virtual memory
8817476.0
max residence set size
8558084.0
stage attributes
key
value
starexec-result
MAYBE
output
124.16/123.48 MAYBE 124.16/123.49 We consider the system theBenchmark. 124.16/123.49 124.16/123.49 Alphabet: 124.16/123.49 124.16/123.49 0 : [] --> N 124.16/123.49 false : [] --> B 124.16/123.49 g : [] --> N -> B 124.16/123.49 g2 : [] --> N -> B 124.16/123.49 geq : [] --> N -> N -> B 124.16/123.49 h : [] --> N -> (N -> B) -> N -> B 124.16/123.49 h2 : [] --> N -> (N -> B) -> N -> B 124.16/123.49 iszero : [] --> N -> N -> B 124.16/123.49 pred : [] --> N -> N 124.16/123.49 rec : [] --> (N -> (N -> B) -> N -> B) -> B -> N -> B 124.16/123.49 s : [] --> N -> N 124.16/123.49 true : [] --> B 124.16/123.49 124.16/123.49 Rules: 124.16/123.49 124.16/123.49 rec f (i 0) => i 124.16/123.49 rec f (i (s x)) => f x (rec f (i x)) 124.16/123.49 g x => true 124.16/123.49 h x f y => false 124.16/123.49 iszero x y => rec h (g x) y 124.16/123.49 pred 0 => 0 124.16/123.49 pred (s x) => x 124.16/123.49 g2 x => iszero x 0 124.16/123.49 h2 x f y => f (pred y) 124.16/123.49 geq x y => rec h2 (g2 x) y 124.16/123.49 124.16/123.49 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. 124.16/123.49 124.16/123.49 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: 124.16/123.49 124.16/123.49 Alphabet: 124.16/123.49 124.16/123.49 0 : [] --> N 124.16/123.49 false : [] --> B 124.16/123.49 g : [] --> N -> B 124.16/123.49 g2 : [] --> N -> B 124.16/123.49 geq : [N] --> N -> B 124.16/123.49 h : [] --> N -> (N -> B) -> N -> B 124.16/123.49 h2 : [] --> N -> (N -> B) -> N -> B 124.16/123.49 iszero : [N] --> N -> B 124.16/123.49 pred : [N] --> N 124.16/123.49 rec : [N -> (N -> B) -> N -> B * B] --> N -> B 124.16/123.49 s : [N] --> N 124.16/123.49 true : [] --> B 124.16/123.49 ~AP1 : [N -> B * N] --> B 124.16/123.49 124.16/123.49 Rules: 124.16/123.49 124.16/123.49 rec(F, ~AP1(G, 0)) => G 124.16/123.49 rec(F, ~AP1(G, s(X))) => F X rec(F, ~AP1(G, X)) 124.16/123.49 g X => true 124.16/123.49 h X F Y => false 124.16/123.49 iszero(X) Y => ~AP1(rec(h, g X), Y) 124.16/123.49 pred(0) => 0 124.16/123.49 pred(s(X)) => X 124.16/123.49 g2 X => iszero(X) 0 124.16/123.49 h2 X F Y => ~AP1(F, pred(Y)) 124.16/123.49 geq(X) Y => ~AP1(rec(h2, g2 X), Y) 124.16/123.49 rec(F, g 0) => g 124.16/123.49 rec(F, g2 0) => g2 124.16/123.49 rec(F, geq(X) 0) => geq(X) 124.16/123.49 rec(F, h X G 0) => h X G 124.16/123.49 rec(F, h2 X G 0) => h2 X G 124.16/123.49 rec(F, iszero(X) 0) => iszero(X) 124.16/123.49 rec(F, g s(X)) => F X rec(F, g X) 124.16/123.49 rec(F, g2 s(X)) => F X rec(F, g2 X) 124.16/123.49 rec(F, geq(X) s(Y)) => F Y rec(F, geq(X) Y) 124.16/123.49 rec(F, h X G s(Y)) => F Y rec(F, h X G Y) 124.16/123.49 rec(F, h2 X G s(Y)) => F Y rec(F, h2 X G Y) 124.16/123.49 rec(F, iszero(X) s(Y)) => F Y rec(F, iszero(X) Y) 124.16/123.49 ~AP1(F, X) => F X 124.16/123.49 124.16/123.49 124.16/123.49 +++ Citations +++ 124.16/123.49 124.16/123.49 [Kop11] C. Kop. Simplifying Algebraic Functional Systems. In Proceedings of CAI 2011, volume 6742 of LNCS. 201--215, Springer, 2011. 124.81/124.13 EOF
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