Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
SRS Standard pair #487083256
details
property
value
status
complete
benchmark
x08.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
Secret_07_SRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
8.68341 seconds
cpu usage
31.2127
user time
29.7829
system time
1.42978
max virtual memory
7.890222E7
max residence set size
3661388.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 17 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 426 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 223 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 202 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(x1) -> x1 a(b(a(x1))) -> a(x1) b(a(a(b(x1)))) -> a(a(a(a(b(b(b(x1))))))) a(a(a(a(x1)))) -> 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(a(a(b(x1)))) -> A(a(a(a(b(b(b(x1))))))) B(a(a(b(x1)))) -> A(a(a(b(b(b(x1)))))) B(a(a(b(x1)))) -> A(a(b(b(b(x1))))) B(a(a(b(x1)))) -> A(b(b(b(x1)))) B(a(a(b(x1)))) -> B(b(b(x1))) B(a(a(b(x1)))) -> B(b(x1)) A(a(a(a(x1)))) -> B(x1) The TRS R consists of the following rules: a(x1) -> x1 a(b(a(x1))) -> a(x1) b(a(a(b(x1)))) -> a(a(a(a(b(b(b(x1))))))) a(a(a(a(x1)))) -> b(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. B(a(a(b(x1)))) -> A(a(b(b(b(x1))))) B(a(a(b(x1)))) -> A(b(b(b(x1)))) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(B(x_1)) = [[0A]] + [[0A, 0A, 1A]] * x_1 >>> <<< POL(a(x_1)) = [[1A], [0A], [0A]] + [[0A, -I, 0A], [1A, 0A, 0A], [0A, 0A, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[0A], [-I], [0A]] + [[-I, 0A, -I], [-I, 0A, -I], [0A, 1A, 0A]] * x_1 >>> <<< POL(A(x_1)) = [[0A]] + [[0A, 0A, 0A]] * x_1 >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: a(a(a(a(x1)))) -> b(x1) b(a(a(b(x1)))) -> a(a(a(a(b(b(b(x1))))))) a(b(a(x1))) -> a(x1) a(x1) -> x1
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to SRS Standard