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SRS Standard pair #516974710
details
property
value
status
complete
benchmark
size-12-alpha-3-num-502.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n067.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
5.09293007851 seconds
cpu usage
16.905594255
max memory
1.266819072E9
stage attributes
key
value
output-size
4397
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 28 ms] (4) QDP (5) MRRProof [EQUIVALENT, 76 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 82 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(x1)) -> b(b(x1)) a(b(x1)) -> c(c(x1)) b(c(x1)) -> a(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(x1)) -> b(b(x1)) b(a(x1)) -> c(c(x1)) c(b(x1)) -> a(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(x1)) -> B(b(x1)) A(a(x1)) -> B(x1) B(a(x1)) -> C(c(x1)) B(a(x1)) -> C(x1) C(b(x1)) -> A(a(x1)) C(b(x1)) -> A(x1) The TRS R consists of the following rules: a(a(x1)) -> b(b(x1)) b(a(x1)) -> c(c(x1)) c(b(x1)) -> a(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(x1)) -> B(x1) B(a(x1)) -> C(x1) C(b(x1)) -> A(x1) Used ordering: Polynomial interpretation [POLO]: POL(A(x_1)) = 2*x_1 POL(B(x_1)) = 2*x_1 POL(C(x_1)) = 2*x_1 POL(a(x_1)) = 2 + 2*x_1
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