Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Higher Order Rewriting Union Beta pair #487094071
details
property
value
status
complete
benchmark
Applicative_AG01_innermost__#4.26.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda 2.2a
configuration
default
runtime (wallclock)
0.506489 seconds
cpu usage
0.465208
user time
0.399852
system time
0.065356
max virtual memory
113188.0
max residence set size
11548.0
stage attributes
key
value
starexec-result
YES
output
YES We consider the system theBenchmark. Alphabet: 0 : [] --> b cons : [c * d] --> d false : [] --> a filter : [c -> a * d] --> d filter2 : [a * c -> a * c * d] --> d if : [a * b * b] --> b le : [b * b] --> a map : [c -> c * d] --> d minus : [b * b] --> b nil : [] --> d p : [b] --> b s : [b] --> b true : [] --> a Rules: p(0) => 0 p(s(x)) => x le(0, x) => true le(s(x), 0) => false le(s(x), s(y)) => le(x, y) minus(x, y) => if(le(x, y), x, y) if(true, x, y) => 0 if(false, x, y) => s(minus(p(x), y)) map(f, nil) => nil map(f, cons(x, y)) => cons(f x, map(f, y)) filter(f, nil) => nil filter(f, cons(x, y)) => filter2(f x, f, x, y) filter2(true, f, x, y) => cons(x, filter(f, y)) filter2(false, f, x, y) => filter(f, y) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We observe that the rules contain a first-order subset: p(0) => 0 p(s(X)) => X le(0, X) => true le(s(X), 0) => false le(s(X), s(Y)) => le(X, Y) minus(X, Y) => if(le(X, Y), X, Y) if(true, X, Y) => 0 if(false, X, Y) => s(minus(p(X), Y)) Moreover, the system is orthogonal. 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 terminating when seen as a many-sorted first-order TRS. According to the external first-order termination prover, this system is indeed terminating: || Input TRS: || 1: p(0()) -> 0() || 2: p(s(PeRCenTX)) -> PeRCenTX || 3: le(0(),PeRCenTX) -> true() || 4: le(s(PeRCenTX),0()) -> false() || 5: le(s(PeRCenTX),s(PeRCenTY)) -> le(PeRCenTX,PeRCenTY) || 6: minus(PeRCenTX,PeRCenTY) -> if(le(PeRCenTX,PeRCenTY),PeRCenTX,PeRCenTY) || 7: if(true(),PeRCenTX,PeRCenTY) -> 0() || 8: if(false(),PeRCenTX,PeRCenTY) -> s(minus(p(PeRCenTX),PeRCenTY)) || Number of strict rules: 8 || Direct POLO(bPol) ... failed. || Uncurrying ... failed. || Dependency Pairs: || #1: #minus(PeRCenTX,PeRCenTY) -> #if(le(PeRCenTX,PeRCenTY),PeRCenTX,PeRCenTY) || #2: #minus(PeRCenTX,PeRCenTY) -> #le(PeRCenTX,PeRCenTY) || #3: #le(s(PeRCenTX),s(PeRCenTY)) -> #le(PeRCenTX,PeRCenTY) || #4: #if(false(),PeRCenTX,PeRCenTY) -> #minus(p(PeRCenTX),PeRCenTY) || #5: #if(false(),PeRCenTX,PeRCenTY) -> #p(PeRCenTX) || Number of SCCs: 2, DPs: 3 || SCC { #3 } || POLO(Sum)... succeeded. || le w: 0 || s w: x1 + 1 || #le w: x1 + x2 || minus w: 0 || false w: 0 || #p w: 0 || true w: 0 || p w: 0 || 0 w: 0 || if w: 0 || #minus w: 0 || #if w: 0 || USABLE RULES: { } || Removed DPs: #3 || Number of SCCs: 1, DPs: 2 || SCC { #1 #4 } || POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. || le w: max(x1 + 1, 0) || s w: max(x1 + 2, 0) || #le w: 0 || minus w: max(x2 - 1, 0) || false w: 3 || #p w: max(x1 - 1, 0) || true w: 1 || p w: max(x1 - 1, 0) || 0 w: 0
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Higher Order Rewriting Union Beta