details

property	value
status	complete
benchmark	size-12-alpha-3-num-435.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n090.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.88519501686 seconds
cpu usage	19.896903115
max memory	1.35163904E9

stage attributes

key	value
output-size	5720
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 25 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 161 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 61 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 41 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(x1) -> b(b(c(x1))) c(a(b(x1))) -> a(a(c(x1))) c(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(x1) -> C(x1) C(a(b(x1))) -> A(a(c(x1))) C(a(b(x1))) -> A(c(x1)) C(a(b(x1))) -> C(x1) The TRS R consists of the following rules: a(x1) -> b(b(c(x1))) c(a(b(x1))) -> a(a(c(x1))) c(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. C(a(b(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)) = [[0A]] + [[0A, 0A, 1A]] * x_1 >>> <<< POL(C(x_1)) = [[0A]] + [[0A, 0A, -I]] * x_1 >>> <<< POL(a(x_1)) = [[0A], [0A], [0A]] + [[0A, 0A, 1A], [0A, 0A, 0A], [0A, -I, -I]] * x_1 >>> <<< POL(b(x_1)) = [[-I], [0A], [0A]] + [[0A, 0A, 0A], [0A, 0A, 0A], [0A, 0A, 0A]] * x_1 >>> <<< POL(c(x_1)) = [[0A], [0A], [-I]] + [[0A, -I, -I], [0A, -I, -I], [0A, -I, -I]] * x_1 >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: c(a(b(x1))) -> a(a(c(x1))) c(b(x1)) -> x1 popout

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