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TRS Standard pair #487068432
details
property
value
status
complete
benchmark
z10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n185.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
5.75642 seconds
cpu usage
21.4317
user time
19.9674
system time
1.46426
max virtual memory
5659436.0
max residence set size
176248.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t())))) a(p(x,y),z) -> p(a(x,z),a(y,z)) a(a(x,y),z) -> a(x,a(y,z)) a(id(),x) -> x a(1(),id()) -> 1() a(t(),id()) -> t() a(1(),p(x,y)) -> x a(t(),p(x,y)) -> y Proof: DP Processor: DPs: a#(lambda(x),y) -> a#(y,t()) a#(lambda(x),y) -> a#(x,p(1(),a(y,t()))) a#(p(x,y),z) -> a#(y,z) a#(p(x,y),z) -> a#(x,z) a#(a(x,y),z) -> a#(y,z) a#(a(x,y),z) -> a#(x,a(y,z)) TRS: a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t())))) a(p(x,y),z) -> p(a(x,z),a(y,z)) a(a(x,y),z) -> a(x,a(y,z)) a(id(),x) -> x a(1(),id()) -> 1() a(t(),id()) -> t() a(1(),p(x,y)) -> x a(t(),p(x,y)) -> y Maximal Polynomial Processor: usable rules: a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t())))) a(p(x,y),z) -> p(a(x,z),a(y,z)) a(a(x,y),z) -> a(x,a(y,z)) a(id(),x) -> x a(1(),id()) -> 1() a(t(),id()) -> t() a(1(),p(x,y)) -> x a(t(),p(x,y)) -> y interpretations: a#(x0, x1) = max(0, 0 + 1 + x0 + -1 + x1) id = 0 p(x0, x1) = max(0, x0, x1) t = 0 1 = 0 a(x0, x1) = max(0, 0 + x0 + x1) lambda(x0) = max(0, 1 + x0) problem: DPs: a#(p(x,y),z) -> a#(y,z) a#(p(x,y),z) -> a#(x,z) a#(a(x,y),z) -> a#(y,z) a#(a(x,y),z) -> a#(x,a(y,z)) TRS: a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t())))) a(p(x,y),z) -> p(a(x,z),a(y,z)) a(a(x,y),z) -> a(x,a(y,z)) a(id(),x) -> x a(1(),id()) -> 1() a(t(),id()) -> t() a(1(),p(x,y)) -> x a(t(),p(x,y)) -> y Restore Modifier: DPs: a#(p(x,y),z) -> a#(y,z) a#(p(x,y),z) -> a#(x,z) a#(a(x,y),z) -> a#(y,z) a#(a(x,y),z) -> a#(x,a(y,z)) TRS: a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t())))) a(p(x,y),z) -> p(a(x,z),a(y,z)) a(a(x,y),z) -> a(x,a(y,z)) a(id(),x) -> x a(1(),id()) -> 1() a(t(),id()) -> t() a(1(),p(x,y)) -> x a(t(),p(x,y)) -> y Subterm Criterion Processor: simple projection: pi(a#) = 0 problem: DPs: TRS: a(lambda(x),y) -> lambda(a(x,p(1(),a(y,t())))) a(p(x,y),z) -> p(a(x,z),a(y,z)) a(a(x,y),z) -> a(x,a(y,z)) a(id(),x) -> x a(1(),id()) -> 1() a(t(),id()) -> t() a(1(),p(x,y)) -> x a(t(),p(x,y)) -> y Qed
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