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HRS union beta 16688 pair #381734215
details
property
value
status
complete
benchmark
fuhkop12rta2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
Kop_13
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.959403991699 seconds
cpu usage
2.033338367
max memory
8.677376E7
stage attributes
key
value
output-size
13653
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 : [] --> nat build : [nat] --> list collapse : [list] --> nat cons : [nat -> nat * list] --> list diff : [nat * nat] --> nat gcd : [nat * nat] --> nat min : [nat * nat] --> nat nil : [] --> list s : [nat] --> nat Rules: min(x, 0) => 0 min(0, x) => 0 min(s(x), s(y)) => s(min(x, y)) diff(x, 0) => x diff(0, x) => x diff(s(x), s(y)) => diff(x, y) gcd(s(x), 0) => s(x) gcd(0, s(x)) => s(x) gcd(s(x), s(y)) => gcd(diff(x, y), s(min(x, y))) collapse(nil) => 0 collapse(cons(f, x)) => f collapse(x) build(0) => nil build(s(x)) => cons(/\y.gcd(y, x), build(x)) 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: min(X, 0) => 0 min(0, X) => 0 min(s(X), s(Y)) => s(min(X, Y)) diff(X, 0) => X diff(0, X) => X diff(s(X), s(Y)) => diff(X, Y) gcd(s(X), 0) => s(X) gcd(0, s(X)) => s(X) gcd(s(X), s(Y)) => gcd(diff(X, Y), s(min(X, Y))) Moreover, the system is finitely branching. 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 Ce-terminating when seen as a many-sorted first-order TRS. According to the external first-order termination prover, this system is indeed Ce-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) DependencyPairsProof [EQUIVALENT] || (2) QDP || (3) DependencyGraphProof [EQUIVALENT] || (4) AND || (5) QDP || (6) UsableRulesProof [EQUIVALENT] || (7) QDP || (8) QDPSizeChangeProof [EQUIVALENT] || (9) YES || (10) QDP || (11) UsableRulesProof [EQUIVALENT] || (12) QDP || (13) QDPSizeChangeProof [EQUIVALENT] || (14) YES || (15) QDP || (16) QDPOrderProof [EQUIVALENT] || (17) QDP || (18) PisEmptyProof [EQUIVALENT] || (19) YES || || || ---------------------------------------- || || (0) || Obligation: || Q restricted rewrite system: || The TRS R consists of the following rules: || || min(%X, 0) -> 0 || min(0, %X) -> 0 || min(s(%X), s(%Y)) -> s(min(%X, %Y)) || diff(%X, 0) -> %X || diff(0, %X) -> %X || diff(s(%X), s(%Y)) -> diff(%X, %Y) || gcd(s(%X), 0) -> s(%X) || gcd(0, s(%X)) -> s(%X) || gcd(s(%X), s(%Y)) -> gcd(diff(%X, %Y), s(min(%X, %Y))) || ~PAIR(%X, %Y) -> %X
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