details

property	value
status	complete
benchmark	ex4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	INVY_15

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.24809 seconds
cpu usage	4.12438
user time	3.94347
system time	0.180903
max virtual memory	1.8478552E7
max residence set size	269888.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 43 ms] (2) RelTRS (3) RIsEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a -> b The relative TRS consists of the following S rules: f(s(x)) -> c(x, f(x)) c(x, c(y, z)) -> c(y, c(x, z)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(a) = [[1], [1]] >>> <<< POL(b) = [[0], [1]] >>> <<< POL(f(x_1)) = [[0], [0]] + [[1, 1], [0, 0]] * x_1 >>> <<< POL(s(x_1)) = [[0], [0]] + [[1, 1], [1, 1]] * x_1 >>> <<< POL(c(x_1, x_2)) = [[0], [0]] + [[1, 1], [0, 0]] * x_1 + [[1, 0], [0, 0]] * x_2 >>> <<< POL(y) = [[0], [0]] >>> <<< POL(z) = [[0], [1]] >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: a -> b Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: R is empty. The relative TRS consists of the following S rules: f(s(x)) -> c(x, f(x)) c(x, c(y, z)) -> c(y, c(x, z)) ---------------------------------------- (3) RIsEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES popout

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job log

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actions

all output return to TRS Relative