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	n089.star.cs.uiowa.edu
space	INVY_15

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.94461393356 seconds
cpu usage	4.460827276
max memory	2.44514816E8

stage attributes

key	value
output-size	1946
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 50 ms] (2) RelTRS (3) RIsEmptyProof [EQUIVALENT, 1 ms] (4)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

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Relat 75837