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Higher Order Rewriting Union Beta pair #487093755
details
property
value
status
complete
benchmark
h19.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Hamana_Kikuchi_18
run statistics
property
value
solver
Wanda 2.2a
configuration
default
runtime (wallclock)
2.03855 seconds
cpu usage
3.44893
user time
3.1089
system time
0.340039
max virtual memory
726604.0
max residence set size
26768.0
stage attributes
key
value
starexec-result
YES
output
YES We consider the system theBenchmark. Alphabet: 0 : [] --> A active : [] --> A -> A app : [] --> (A -> A) -> A -> A cons : [] --> A -> A -> A from : [] --> A -> A map : [] --> (A -> A) -> A -> A mark : [] --> A -> A minus : [] --> A -> A -> A nil : [] --> A quot : [] --> A -> A -> A s : [] --> A -> A sel : [] --> A -> A -> A zWquot : [] --> A -> A -> A Rules: active (from x) => mark (cons x (from (s x))) active (sel 0 (cons x y)) => mark x active (sel (s x) (cons y z)) => mark (sel x z) active (minus x 0) => mark 0 active (minus (s x) (s y)) => mark (minus x y) active (quot 0 (s x)) => mark 0 active (quot (s x) (s y)) => mark (s (quot (minus x y) (s y))) active (zWquot x nil) => mark nil active (zWquot nil x) => mark nil active (zWquot (cons x y) (cons z u)) => mark (cons (quot x z) (zWquot y u)) mark (from x) => active (from (mark x)) mark (cons x y) => active (cons (mark x) y) mark (s x) => active (s (mark x)) mark (sel x y) => active (sel (mark x) (mark y)) mark 0 => active 0 mark (minus x y) => active (minus (mark x) (mark y)) mark (quot x y) => active (quot (mark x) (mark y)) mark (zWquot x y) => active (zWquot (mark x) (mark y)) mark nil => active nil from (mark x) => from x from (active x) => from x cons (mark x) y => cons x y cons x (mark y) => cons x y cons (active x) y => cons x y cons x (active y) => cons x y s (mark x) => s x s (active x) => s x sel (mark x) y => sel x y sel x (mark y) => sel x y sel (active x) y => sel x y sel x (active y) => sel x y minus (mark x) y => minus x y minus x (mark y) => minus x y minus (active x) y => minus x y minus x (active y) => minus x y quot (mark x) y => quot x y quot x (mark y) => quot x y quot (active x) y => quot x y quot x (active y) => quot x y zWquot (mark x) y => zWquot x y zWquot x (mark y) => zWquot x y zWquot (active x) y => zWquot x y zWquot x (active y) => zWquot x y map (/\x.f x) nil => nil app (/\x.f x) y => f y 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: 0 : [] --> A active : [A] --> A app : [A -> A * A] --> A cons : [A * A] --> A from : [A] --> A map : [A -> A * A] --> A mark : [A] --> A minus : [A * A] --> A nil : [] --> A quot : [A * A] --> A s : [A] --> A sel : [A * A] --> A zWquot : [A * A] --> A ~AP1 : [A -> A * A] --> A Rules: active(from(X)) => mark(cons(X, from(s(X)))) active(sel(0, cons(X, Y))) => mark(X) active(sel(s(X), cons(Y, Z))) => mark(sel(X, Z)) active(minus(X, 0)) => mark(0) active(minus(s(X), s(Y))) => mark(minus(X, Y)) active(quot(0, s(X))) => mark(0) active(quot(s(X), s(Y))) => mark(s(quot(minus(X, Y), s(Y)))) active(zWquot(X, nil)) => mark(nil) active(zWquot(nil, X)) => mark(nil) active(zWquot(cons(X, Y), cons(Z, U))) => mark(cons(quot(X, Z), zWquot(Y, U)))
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