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SRS Stand 10685 pair #381721809
details
property
value
status
complete
benchmark
size-12-alpha-3-num-40.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.28028202057 seconds
cpu usage
13.198251868
max memory
1.275236352E9
stage attributes
key
value
output-size
5480
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 14 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 115 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 6 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 15 ms] (10) QDP (11) PisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(x1) -> x1 a(x1) -> b(b(c(x1))) c(c(a(x1))) -> a(a(c(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: A(x1) -> C(x1) C(c(a(x1))) -> A(a(c(c(x1)))) C(c(a(x1))) -> A(c(c(x1))) C(c(a(x1))) -> C(c(x1)) C(c(a(x1))) -> C(x1) The TRS R consists of the following rules: a(x1) -> x1 a(x1) -> b(b(c(x1))) c(c(a(x1))) -> a(a(c(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. A(x1) -> C(x1) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(A(x_1)) = [[1A]] + [[0A, 1A, 1A]] * x_1 >>> <<< POL(C(x_1)) = [[0A]] + [[-I, 0A, 0A]] * x_1 >>> <<< POL(c(x_1)) = [[0A], [0A], [0A]] + [[-I, 0A, -I], [1A, -I, 0A], [0A, -I, -I]] * x_1 >>> <<< POL(a(x_1)) = [[1A], [-I], [0A]] + [[0A, 1A, -I], [-I, 0A, -I], [-I, -I, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[0A], [-I], [-I]] + [[-I, -I, -I], [-I, -I, -I], [0A, 0A, -I]] * x_1 >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
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