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SRS Standard pair #487085014
details
property
value
status
complete
benchmark
size-12-alpha-3-num-472.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
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.75357 seconds
cpu usage
19.7783
user time
18.9134
system time
0.864908
max virtual memory
5.8208428E7
max residence set size
2418804.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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, 1 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 363 ms] (6) QDP (7) UsableRulesProof [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(a(x1)) -> x1 b(b(x1)) -> c(c(c(x1))) b(c(x1)) -> a(b(b(x1))) Q is empty. ---------------------------------------- (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: B(c(x1)) -> A(b(b(x1))) B(c(x1)) -> B(b(x1)) B(c(x1)) -> B(x1) The TRS R consists of the following rules: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(x1))) b(c(x1)) -> a(b(b(x1))) Q is empty. 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 1 less node. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: B(c(x1)) -> B(x1) B(c(x1)) -> B(b(x1)) The TRS R consists of the following rules: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(x1))) b(c(x1)) -> a(b(b(x1))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. B(c(x1)) -> B(b(x1)) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic integers [ARCTIC,STERNAGEL_THIEMANN_RTA14]: <<< POL(B(x_1)) = [[0A]] + [[-1A, -1A, -1A]] * x_1 >>> <<< POL(c(x_1)) = [[2A], [-I], [0A]] + [[0A, -1A, 0A], [-I, -1A, -I], [-I, 2A, -I]] * x_1 >>> <<< POL(b(x_1)) = [[0A], [1A], [-I]] + [[-1A, 1A, -1A], [-1A, 1A, -1A], [-1A, -1A, -1A]] * x_1
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