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TRS Stand 20472 pair #381713397
details
property
value
status
complete
benchmark
tpa03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
12.3865509033 seconds
cpu usage
18.945267453
max memory
2.023112704E9
stage attributes
key
value
output-size
8165
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 34 ms] (4) QDP (5) RootLabelingFC2Proof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) MRRProof [EQUIVALENT, 0 ms] (10) QDP (11) SemLabProof [SOUND, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, f(y, x)) -> f(f(x, x), f(a, y)) 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: F(x, f(y, x)) -> F(f(x, x), f(a, y)) F(x, f(y, x)) -> F(x, x) F(x, f(y, x)) -> F(a, y) The TRS R consists of the following rules: f(x, f(y, x)) -> f(f(x, x), f(a, y)) 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. F(x, f(y, x)) -> F(x, x) F(x, f(y, x)) -> F(a, y) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(F(x_1, x_2)) = [[0A]] + [[0A]] * x_1 + [[0A]] * x_2 >>> <<< POL(f(x_1, x_2)) = [[1A]] + [[1A]] * x_1 + [[1A]] * x_2 >>> <<< POL(a) = [[0A]] >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: f(x, f(y, x)) -> f(f(x, x), f(a, y)) ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules:
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