details

property	value
status	complete
benchmark	tpa01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.52803 seconds
cpu usage	6.90894
user time	6.58713
system time	0.321809
max virtual memory	1.8554208E7
max residence set size	429984.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 34 ms] (4) QDP (5) QDPBoundsTAProof [EQUIVALENT, 140 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(y, x)) -> f(f(a, y), f(a, y)) 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(y, x)) -> F(f(a, y), f(a, y)) F(y, f(y, x)) -> F(a, y) The TRS R consists of the following rules: f(y, f(y, x)) -> f(f(a, y), f(a, y)) 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(y, x)) -> F(a, y) 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 + [[4A]] * 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(y, x)) -> f(f(a, y), f(a, y)) ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(y, f(y, x)) -> F(f(a, y), f(a, y)) The TRS R consists of the following rules: f(y, f(y, x)) -> f(f(a, y), f(a, y)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPBoundsTAProof (EQUIVALENT) The DP-Problem (P, R) could be shown to be Match-(raise-)DP-Bounded [TAB_NONLEFTLINEAR] by 2 for the Rule: F(y, f(y, x)) -> F(f(a, y), f(a, y)) by considering the usable rules: popout

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

job log

popout

actions

all output return to TRS Standard