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HRS union beta 16688 pair #381734920
details
property
value
status
complete
benchmark
Applicative_first_order_05__21.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n191.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.944065093994 seconds
cpu usage
1.771464386
max memory
1.15871744E8
stage attributes
key
value
output-size
18627
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: !facplus : [a * a] --> a !factimes : [a * a] --> a 0 : [] --> a cons : [c * d] --> d fact : [a] --> a false : [] --> b filter : [c -> b * d] --> d filter2 : [b * c -> b * c * d] --> d map : [c -> c * d] --> d nil : [] --> d p : [a] --> a s : [a] --> a true : [] --> b Rules: p(s(x)) => x fact(0) => s(0) fact(s(x)) => !factimes(s(x), fact(p(s(x)))) !factimes(0, x) => 0 !factimes(s(x), y) => !facplus(!factimes(x, y), y) !facplus(x, 0) => x !facplus(x, s(y)) => s(!facplus(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(s(X)) => X fact(0) => s(0) fact(s(X)) => !factimes(s(X), fact(p(s(X)))) !factimes(0, X) => 0 !factimes(s(X), Y) => !facplus(!factimes(X, Y), Y) !facplus(X, 0) => X !facplus(X, s(Y)) => s(!facplus(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) Overlay + Local Confluence [EQUIVALENT] || (2) QTRS || (3) DependencyPairsProof [EQUIVALENT] || (4) QDP || (5) DependencyGraphProof [EQUIVALENT] || (6) AND || (7) QDP || (8) UsableRulesProof [EQUIVALENT] || (9) QDP || (10) QReductionProof [EQUIVALENT] || (11) QDP || (12) QDPSizeChangeProof [EQUIVALENT] || (13) YES || (14) QDP || (15) UsableRulesProof [EQUIVALENT] || (16) QDP || (17) QReductionProof [EQUIVALENT] || (18) QDP || (19) QDPSizeChangeProof [EQUIVALENT] || (20) YES || (21) QDP || (22) UsableRulesProof [EQUIVALENT] || (23) QDP || (24) QReductionProof [EQUIVALENT] || (25) QDP || (26) MRRProof [EQUIVALENT] || (27) QDP || (28) DependencyGraphProof [EQUIVALENT] || (29) TRUE || || || ---------------------------------------- || || (0) || Obligation: || Q restricted rewrite system:
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