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SRS Standard pair #487511681
details
property
value
status
complete
benchmark
01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n127.star.cs.uiowa.edu
space
Mixed_SRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.03646302223 seconds
cpu usage
16.935994225
max memory
2.315042816E9
stage attributes
key
value
output-size
4236
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 21 ms] (4) QDP (5) MRRProof [EQUIVALENT, 19 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 216 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(a(x1)))) -> a(b(a(b(x1)))) b(a(b(x1))) -> a(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(a(x1)))) -> b(a(b(a(x1)))) b(a(b(x1))) -> a(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(a(x1)))) -> B(a(b(a(x1)))) A(a(a(a(x1)))) -> A(b(a(x1))) A(a(a(a(x1)))) -> B(a(x1)) B(a(b(x1))) -> A(b(a(x1))) B(a(b(x1))) -> B(a(x1)) B(a(b(x1))) -> A(x1) The TRS R consists of the following rules: a(a(a(a(x1)))) -> b(a(b(a(x1)))) b(a(b(x1))) -> a(b(a(x1))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: A(a(a(a(x1)))) -> A(b(a(x1))) A(a(a(a(x1)))) -> B(a(x1)) B(a(b(x1))) -> B(a(x1)) B(a(b(x1))) -> A(x1) Used ordering: Polynomial interpretation [POLO]: POL(A(x_1)) = 2 + 2*x_1 POL(B(x_1)) = 2 + 2*x_1 POL(a(x_1)) = 1 + x_1 POL(b(x_1)) = 1 + x_1
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