details

property	value
status	complete
benchmark	tpa02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.88986301422 seconds
cpu usage	7.450364296
max memory	4.08322048E8

stage attributes

key	value
output-size	5927
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 33 ms] (4) QDP (5) QDPBoundsTAProof [EQUIVALENT, 131 ms] (6) QDP (7) PisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(y, f(x, y)) -> f(f(a, y), f(a, x)) 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: F(y, f(x, y)) -> F(f(a, y), f(a, x)) F(y, f(x, y)) -> F(a, y) F(y, f(x, y)) -> F(a, x) The TRS R consists of the following rules: f(y, f(x, y)) -> f(f(a, y), f(a, x)) 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. F(y, f(x, y)) -> F(a, y) F(y, f(x, y)) -> F(a, x) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(F(x_1, x_2)) = [[0A]] + [[0A]] * x_1 + [[2A]] * x_2 >>> <<< POL(f(x_1, x_2)) = [[1A]] + [[1A]] * x_1 + [[1A]] * x_2 >>> <<< POL(a) = [[0A]] >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: f(y, f(x, y)) -> f(f(a, y), f(a, x)) ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(y, f(x, y)) -> F(f(a, y), f(a, x)) The TRS R consists of the following rules: f(y, f(x, y)) -> f(f(a, y), f(a, x)) popout

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