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SRS Stand 10685 pair #381720059
details
property
value
status
complete
benchmark
size-12-alpha-2-num-22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n104.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.48015713692 seconds
cpu usage
13.836418503
max memory
1.39380736E9
stage attributes
key
value
output-size
2996
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 3 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 164 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(x1) -> x1 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) b(x1) -> a(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: A(a(b(a(x1)))) -> B(b(a(a(a(x1))))) A(a(b(a(x1)))) -> B(a(a(a(x1)))) A(a(b(a(x1)))) -> A(a(a(x1))) A(a(b(a(x1)))) -> A(a(x1)) B(x1) -> A(x1) The TRS R consists of the following rules: a(x1) -> x1 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) b(x1) -> a(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. A(a(b(a(x1)))) -> B(b(a(a(a(x1))))) A(a(b(a(x1)))) -> B(a(a(a(x1)))) A(a(b(a(x1)))) -> A(a(a(x1))) A(a(b(a(x1)))) -> A(a(x1)) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(A(x_1)) = [[0A]] + [[-I, -I, 0A]] * x_1 >>> <<< POL(a(x_1)) = [[-I], [0A], [-I]] + [[0A, -I, 0A], [0A, 0A, 0A], [0A, -I, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[1A], [0A], [-I]] + [[0A, 0A, 1A], [0A, 0A, 0A], [0A, -I, 0A]] * x_1 >>> <<< POL(B(x_1)) = [[0A]] + [[-I, -I, 0A]] * x_1 >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: a(x1) -> x1 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) b(x1) -> a(x1) ----------------------------------------
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