details

property	value
status	complete
benchmark	size-12-alpha-3-num-448.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.93233 seconds
cpu usage	8.65114
user time	8.26934
system time	0.381804
max virtual memory	1.9809944E7
max residence set size	947880.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 91 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(x1) -> b(c(x1)) a(b(b(x1))) -> b(b(a(a(x1)))) c(b(x1)) -> 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: A(x1) -> C(x1) A(b(b(x1))) -> A(a(x1)) A(b(b(x1))) -> A(x1) The TRS R consists of the following rules: a(x1) -> b(c(x1)) a(b(b(x1))) -> b(b(a(a(x1)))) c(b(x1)) -> 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: A(b(b(x1))) -> A(x1) A(b(b(x1))) -> A(a(x1)) The TRS R consists of the following rules: a(x1) -> b(c(x1)) a(b(b(x1))) -> b(b(a(a(x1)))) c(b(x1)) -> 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. A(b(b(x1))) -> A(a(x1)) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(A(x_1)) = [[0A]] + [[-I, 0A, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[1A], [0A], [0A]] + [[0A, 1A, 0A], [0A, 0A, 0A], [-I, 0A, 0A]] * x_1 >>> <<< POL(a(x_1)) = [[1A], [0A], [0A]] + [[0A, 1A, 0A], [-I, 0A, -I], [-I, 0A, -I]] * x_1 popout

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