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HRS union beta 16688 pair #381734809
details
property
value
status
complete
benchmark
Applicative_AG01_innermost__#4.24.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n083.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.93935585022 seconds
cpu usage
2.050354163
max memory
8.945664E7
stage attributes
key
value
output-size
15635
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: 0 : [] --> b cons : [b * c] --> c false : [] --> a filter : [b -> a * c] --> c filter2 : [a * b -> a * b * c] --> c int : [b * b] --> c intlist : [c] --> c map : [b -> b * c] --> c nil : [] --> c s : [b] --> b true : [] --> a Rules: intlist(nil) => nil intlist(cons(x, y)) => cons(s(x), intlist(y)) int(0, 0) => cons(0, nil) int(0, s(x)) => cons(0, int(s(0), s(x))) int(s(x), 0) => nil int(s(x), s(y)) => intlist(int(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: intlist(nil) => nil intlist(cons(X, Y)) => cons(s(X), intlist(Y)) int(0, 0) => cons(0, nil) int(0, s(X)) => cons(0, int(s(0), s(X))) int(s(X), 0) => nil int(s(X), s(Y)) => intlist(int(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: || proof of resources/system.trs || # AProVE Commit ID: d84c10301d352dfd14de2104819581f4682260f5 fuhs 20130616 || || || Termination w.r.t. Q of the given QTRS could be proven: || || (0) QTRS || (1) QTRSRRRProof [EQUIVALENT] || (2) QTRS || (3) QTRSRRRProof [EQUIVALENT] || (4) QTRS || (5) Overlay + Local Confluence [EQUIVALENT] || (6) QTRS || (7) DependencyPairsProof [EQUIVALENT] || (8) QDP || (9) DependencyGraphProof [EQUIVALENT] || (10) AND || (11) QDP || (12) UsableRulesProof [EQUIVALENT] || (13) QDP || (14) QReductionProof [EQUIVALENT] || (15) QDP || (16) QDPSizeChangeProof [EQUIVALENT] || (17) YES || (18) QDP || (19) UsableRulesProof [EQUIVALENT] || (20) QDP || (21) QReductionProof [EQUIVALENT] || (22) QDP || (23) QDPSizeChangeProof [EQUIVALENT] || (24) YES || || || ---------------------------------------- || || (0) || Obligation: || Q restricted rewrite system: || The TRS R consists of the following rules: || || intlist(nil) -> nil || intlist(cons(%X, %Y)) -> cons(s(%X), intlist(%Y)) || int(0, 0) -> cons(0, nil) || int(0, s(%X)) -> cons(0, int(s(0), s(%X))) || int(s(%X), 0) -> nil || int(s(%X), s(%Y)) -> intlist(int(%X, %Y)) ||
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