Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
SRS Standard pair #487085650
details
property
value
status
complete
benchmark
05.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
Bouchare_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.29806 seconds
cpu usage
13.849
user time
13.1105
system time
0.738462
max virtual memory
6.1223496E7
max residence set size
1952144.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 123 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 72 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(b(x1))) -> a(x1) a(a(x1)) -> b(b(b(x1))) b(b(a(x1))) -> a(b(a(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(b(b(x1))) -> A(x1) A(a(x1)) -> B(b(b(x1))) A(a(x1)) -> B(b(x1)) A(a(x1)) -> B(x1) B(b(a(x1))) -> A(b(a(x1))) The TRS R consists of the following rules: a(b(b(x1))) -> a(x1) a(a(x1)) -> b(b(b(x1))) b(b(a(x1))) -> a(b(a(x1))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) 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(x1) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(A(x_1)) = [[-I]] + [[0A, -I, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[0A], [0A], [-I]] + [[0A, 0A, 1A], [-I, 0A, 0A], [0A, -I, 0A]] * x_1 >>> <<< POL(a(x_1)) = [[0A], [0A], [-I]] + [[1A, 0A, 1A], [0A, 0A, 0A], [0A, -I, 0A]] * x_1 >>> <<< POL(B(x_1)) = [[0A]] + [[-I, 0A, 0A]] * x_1 >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: a(a(x1)) -> b(b(b(x1))) b(b(a(x1))) -> a(b(a(x1))) a(b(b(x1))) -> a(x1) ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: A(a(x1)) -> B(b(b(x1)))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to SRS Standard