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SRS Standard pair #516969268
details
property
value
status
complete
benchmark
touzet.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n009.star.cs.uiowa.edu
space
Mixed_SRS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
4.78507494926 seconds
cpu usage
15.615815011
max memory
1.280249856E9
stage attributes
key
value
output-size
2934
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 142 ms] (4)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(b(x1)) -> b(b(b(x1))) b(a(x1)) -> a(a(a(x1))) a(x1) -> x1 b(x1) -> 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(b(x1)) -> B(b(b(x1))) A(b(x1)) -> B(b(x1)) B(a(x1)) -> A(a(a(x1))) B(a(x1)) -> A(a(x1)) The TRS R consists of the following rules: a(b(x1)) -> b(b(b(x1))) b(a(x1)) -> a(a(a(x1))) a(x1) -> x1 b(x1) -> 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. B(a(x1)) -> A(a(a(x1))) 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)) = [[-I]] + [[0A, -I, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[0A], [-I], [-I]] + [[0A, -I, -I], [-I, 0A, -I], [-I, 0A, 0A]] * x_1 >>> <<< POL(B(x_1)) = [[0A]] + [[-I, 0A, 0A]] * x_1 >>> <<< POL(a(x_1)) = [[-I], [0A], [-I]] + [[0A, -I, 0A], [1A, 0A, 1A], [0A, -I, 0A]] * x_1 >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: b(a(x1)) -> a(a(a(x1))) a(b(x1)) -> b(b(b(x1))) b(x1) -> x1 a(x1) -> x1 ----------------------------------------
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