details

property	value
status	complete
benchmark	sym-5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Waldmann_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	85.0092 seconds
cpu usage	330.977
user time	326.306
system time	4.67153
max virtual memory	8.1555616E7
max residence set size	5867076.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 29 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 2547 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(a(x1))) -> b(b(b(x1))) b(b(b(b(x1)))) -> a(b(b(a(x1)))) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(a(x1))) -> b(b(b(x1))) b(b(b(b(x1)))) -> a(b(b(a(x1)))) Q is empty. ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: A(a(a(x1))) -> B(b(b(x1))) A(a(a(x1))) -> B(b(x1)) A(a(a(x1))) -> B(x1) B(b(b(b(x1)))) -> A(b(b(a(x1)))) B(b(b(b(x1)))) -> B(b(a(x1))) B(b(b(b(x1)))) -> B(a(x1)) B(b(b(b(x1)))) -> A(x1) The TRS R consists of the following rules: a(a(a(x1))) -> b(b(b(x1))) b(b(b(b(x1)))) -> a(b(b(a(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(a(a(x1))) -> B(b(x1)) A(a(a(x1))) -> B(x1) B(b(b(b(x1)))) -> B(b(a(x1))) B(b(b(b(x1)))) -> B(a(x1)) B(b(b(b(x1)))) -> A(x1) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(A(x_1)) = 1 + x_1 POL(B(x_1)) = 1 + x_1 POL(a(x_1)) = 1 + x_1 POL(b(x_1)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: b(b(b(b(x1)))) -> a(b(b(a(x1)))) a(a(a(x1))) -> b(b(b(x1))) popout

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