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TRS Innermost pair #487093111
details
property
value
status
complete
benchmark
Ex24_GM04_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.63565 seconds
cpu usage
3.59687
user time
3.43819
system time
0.158681
max virtual memory
1.8343148E7
max residence set size
233784.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) UsableRulesProof [EQUIVALENT, 0 ms] (6) QDP (7) QReductionProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(X, g(X), Y) -> a__f(Y, Y, Y) a__g(b) -> c a__b -> c mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) mark(g(X)) -> a__g(mark(X)) mark(b) -> a__b mark(c) -> c a__f(X1, X2, X3) -> f(X1, X2, X3) a__g(X) -> g(X) a__b -> b The set Q consists of the following terms: a__b mark(f(x0, x1, x2)) mark(g(x0)) mark(b) mark(c) a__f(x0, x1, x2) a__g(x0) ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: A__F(X, g(X), Y) -> A__F(Y, Y, Y) MARK(f(X1, X2, X3)) -> A__F(X1, X2, X3) MARK(g(X)) -> A__G(mark(X)) MARK(g(X)) -> MARK(X) MARK(b) -> A__B The TRS R consists of the following rules: a__f(X, g(X), Y) -> a__f(Y, Y, Y) a__g(b) -> c a__b -> c mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) mark(g(X)) -> a__g(mark(X)) mark(b) -> a__b mark(c) -> c a__f(X1, X2, X3) -> f(X1, X2, X3) a__g(X) -> g(X) a__b -> b The set Q consists of the following terms: a__b mark(f(x0, x1, x2)) mark(g(x0)) mark(b) mark(c) a__f(x0, x1, x2) a__g(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules:
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