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SRS Standard pair #516976576
details
property
value
status
complete
benchmark
random-519.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n169.star.cs.uiowa.edu
space
Waldmann_19
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
25.1233108044 seconds
cpu usage
96.523800566
max memory
2.188177408E9
stage attributes
key
value
output-size
6282
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 68 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) QDPOrderProof [EQUIVALENT, 6913 ms] (9) QDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) QDPOrderProof [EQUIVALENT, 0 ms] (14) QDP (15) PisEmptyProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(b(b(a(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> b(a(b(b(x1)))) b(a(a(a(x1)))) -> a(a(a(b(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: B(b(b(a(x1)))) -> B(b(a(a(x1)))) B(b(b(a(x1)))) -> B(a(a(x1))) B(a(b(a(x1)))) -> B(a(b(b(x1)))) B(a(b(a(x1)))) -> B(b(x1)) B(a(b(a(x1)))) -> B(x1) B(a(a(a(x1)))) -> B(x1) The TRS R consists of the following rules: b(b(b(a(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> b(a(b(b(x1)))) b(a(a(a(x1)))) -> a(a(a(b(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(b(b(a(x1)))) -> B(a(a(x1))) B(a(b(a(x1)))) -> B(b(x1)) B(a(b(a(x1)))) -> B(x1) B(a(a(a(x1)))) -> B(x1) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(B(x_1)) = x_1 POL(a(x_1)) = 1 + x_1 POL(b(x_1)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: b(a(a(a(x1)))) -> a(a(a(b(x1)))) b(b(b(a(x1)))) -> b(b(a(a(x1)))) b(a(b(a(x1)))) -> b(a(b(b(x1)))) ---------------------------------------- (4)
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