details

property	value
status	complete
benchmark	#3.26.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.89453 seconds
cpu usage	8.45316
user time	7.98351
system time	0.469654
max virtual memory	2.0073344E7
max residence set size	1090872.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) MNOCProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 33 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(x) -> s(x) f(s(s(x))) -> s(f(f(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(s(s(x))) -> F(f(x)) F(s(s(x))) -> F(x) The TRS R consists of the following rules: f(x) -> s(x) f(s(s(x))) -> s(f(f(x))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) MNOCProof (EQUIVALENT) We use the modular non-overlap check [LPAR04] to enlarge Q to all left-hand sides of R. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(s(s(x))) -> F(f(x)) F(s(s(x))) -> F(x) The TRS R consists of the following rules: f(x) -> s(x) f(s(s(x))) -> s(f(f(x))) The set Q consists of the following terms: f(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. F(s(s(x))) -> F(f(x)) F(s(s(x))) -> F(x) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: POL( F_1(x_1) ) = x_1 + 2 POL( f_1(x_1) ) = x_1 + 2 POL( s_1(x_1) ) = x_1 + 2 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: f(x) -> s(x) f(s(s(x))) -> s(f(f(x))) ---------------------------------------- popout

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