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SRS Standard pair #487085626
details
property
value
status
complete
benchmark
03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Bouchare_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.93405 seconds
cpu usage
12.6366
user time
12.0617
system time
0.574907
max virtual memory
5.9597704E7
max residence set size
1603036.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 18 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 176 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) UsableRulesProof [EQUIVALENT, 0 ms] (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(b(x1)) -> a(a(a(x1))) a(a(b(x1))) -> b(x1) a(b(a(x1))) -> a(b(b(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: b(b(x1)) -> a(a(a(x1))) b(a(a(x1))) -> b(x1) a(b(a(x1))) -> 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: B(b(x1)) -> A(a(a(x1))) B(b(x1)) -> A(a(x1)) B(b(x1)) -> A(x1) B(a(a(x1))) -> B(x1) A(b(a(x1))) -> B(b(a(x1))) The TRS R consists of the following rules: b(b(x1)) -> a(a(a(x1))) b(a(a(x1))) -> b(x1) a(b(a(x1))) -> 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(b(a(x1))) -> B(b(a(x1))) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(B(x_1)) = [[-I]] + [[0A, -I, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[-I], [-I], [-I]] + [[0A, 0A, 0A], [1A, 0A, -I], [0A, 0A, 0A]] * x_1 >>> <<< POL(A(x_1)) = [[-I]] + [[0A, 0A, 0A]] * x_1 >>>
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