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HRS union beta 16688 pair #381734821
details
property
value
status
complete
benchmark
Applicative_AG01_innermost__#4.34.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.971863985062 seconds
cpu usage
2.105665774
max memory
1.31076096E8
stage attributes
key
value
output-size
14094
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: 0 : [] --> b 1 : [] --> b c : [b] --> b cons : [c * d] --> d f : [b] --> a false : [] --> a filter : [c -> a * d] --> d filter2 : [a * c -> a * c * d] --> d g : [b * b] --> b if : [a * b * b] --> b map : [c -> c * d] --> d nil : [] --> d s : [b] --> b true : [] --> a Rules: f(0) => true f(1) => false f(s(x)) => f(x) if(true, x, y) => x if(false, x, y) => y g(s(x), s(y)) => if(f(x), s(x), s(y)) g(x, c(y)) => g(x, g(s(c(y)), y)) map(h, nil) => nil map(h, cons(x, y)) => cons(h x, map(h, y)) filter(h, nil) => nil filter(h, cons(x, y)) => filter2(h x, h, x, y) filter2(true, h, x, y) => cons(x, filter(h, y)) filter2(false, h, x, y) => filter(h, 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: f(0) => true f(1) => false f(s(X)) => f(X) if(true, X, Y) => X if(false, X, Y) => Y g(s(X), s(Y)) => if(f(X), s(X), s(Y)) g(X, c(Y)) => g(X, g(s(c(Y)), 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) QDPOrderProof [EQUIVALENT] || (16) QDP || (17) PisEmptyProof [EQUIVALENT] || (18) YES || || || ---------------------------------------- || || (0) || Obligation: || Q restricted rewrite system: || The TRS R consists of the following rules: || || f(0) -> true || f(1) -> false || f(s(%X)) -> f(%X) || if(true, %X, %Y) -> %X || if(false, %X, %Y) -> %Y || g(s(%X), s(%Y)) -> if(f(%X), s(%X), s(%Y)) || g(%X, c(%Y)) -> g(%X, g(s(c(%Y)), %Y)) ||
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