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SRS Stand 10685 pair #381718421
details
property
value
status
complete
benchmark
x01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Secret_07_SRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
11.7586970329 seconds
cpu usage
41.910851565
max memory
4.157943808E9
stage attributes
key
value
output-size
6352
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 1 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 144 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 47 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) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(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: C(b(x1)) -> D(x1) E(b(x1)) -> C(c(x1)) E(b(x1)) -> C(x1) D(b(x1)) -> F(x1) F(x1) -> A(e(x1)) F(x1) -> E(x1) A(a(x1)) -> F(x1) The TRS R consists of the following rules: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(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. C(b(x1)) -> D(x1) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(C(x_1)) = [[-I]] + [[0A, 0A, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[0A], [1A], [0A]] + [[0A, 0A, 0A], [0A, 0A, 1A], [0A, -I, 0A]] * x_1 >>> <<< POL(D(x_1)) = [[0A]] + [[-I, -I, 0A]] * x_1 >>> <<< POL(E(x_1)) = [[0A]] + [[0A, -I, 0A]] * x_1
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