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SRS Stand 10685 pair #381718165
details
property
value
status
complete
benchmark
sym-6.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
Waldmann_06_SRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
31.9217610359 seconds
cpu usage
120.379640886
max memory
5.648654336E9
stage attributes
key
value
output-size
7261
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 5 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 1057 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 1399 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 885 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 321 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: c(c(c(c(x1)))) -> b(b(b(b(x1)))) b(b(x1)) -> x1 b(b(x1)) -> c(b(c(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(c(c(c(x1)))) -> B(b(b(b(x1)))) C(c(c(c(x1)))) -> B(b(b(x1))) C(c(c(c(x1)))) -> B(b(x1)) C(c(c(c(x1)))) -> B(x1) B(b(x1)) -> C(b(c(x1))) B(b(x1)) -> B(c(x1)) B(b(x1)) -> C(x1) The TRS R consists of the following rules: c(c(c(c(x1)))) -> b(b(b(b(x1)))) b(b(x1)) -> x1 b(b(x1)) -> c(b(c(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(x1)) -> C(b(c(x1))) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic integers [ARCTIC,STERNAGEL_THIEMANN_RTA14]: <<< POL(C(x_1)) = [[0A]] + [[-1A, -1A, -I]] * x_1 >>> <<< POL(c(x_1)) = [[0A], [0A], [-I]] + [[-1A, 0A, -1A], [-1A, 1A, 0A], [-1A, -I, -I]] * x_1 >>> <<< POL(B(x_1)) = [[1A]] + [[-1A, -I, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[0A], [-I], [0A]] + [[-I, -I, 0A], [-1A, -I, 1A], [0A, -1A, -1A]] * x_1 >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: b(b(x1)) -> x1
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