details

property	value
status	complete
benchmark	Ex1_2_Luc02c_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n128.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.14677 seconds
cpu usage	7.84848
user time	7.49376
system time	0.354725
max virtual memory	1.8484064E7
max residence set size	570412.0

stage attributes

key	value
starexec-result	YES

output

7.69/3.09 YES 7.79/3.11 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 7.79/3.11 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.79/3.11 7.79/3.11 7.79/3.11 Termination w.r.t. Q of the given QTRS could be proven: 7.79/3.11 7.79/3.11 (0) QTRS 7.79/3.11 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 7.79/3.11 (2) QDP 7.79/3.11 (3) QDPOrderProof [EQUIVALENT, 69 ms] 7.79/3.11 (4) QDP 7.79/3.11 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 7.79/3.11 (6) QDP 7.79/3.11 (7) QDPOrderProof [EQUIVALENT, 17 ms] 7.79/3.11 (8) QDP 7.79/3.11 (9) QDPOrderProof [EQUIVALENT, 35 ms] 7.79/3.11 (10) QDP 7.79/3.11 (11) UsableRulesProof [EQUIVALENT, 0 ms] 7.79/3.11 (12) QDP 7.79/3.11 (13) QReductionProof [EQUIVALENT, 0 ms] 7.79/3.11 (14) QDP 7.79/3.11 (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] 7.79/3.11 (16) YES 7.79/3.11 7.79/3.11 7.79/3.11 ---------------------------------------- 7.79/3.11 7.79/3.11 (0) 7.79/3.11 Obligation: 7.79/3.11 Q restricted rewrite system: 7.79/3.11 The TRS R consists of the following rules: 7.79/3.11 7.79/3.11 a__2nd(cons(X, cons(Y, Z))) -> mark(Y) 7.79/3.11 a__from(X) -> cons(mark(X), from(s(X))) 7.79/3.11 mark(2nd(X)) -> a__2nd(mark(X)) 7.79/3.11 mark(from(X)) -> a__from(mark(X)) 7.79/3.11 mark(cons(X1, X2)) -> cons(mark(X1), X2) 7.79/3.11 mark(s(X)) -> s(mark(X)) 7.79/3.11 a__2nd(X) -> 2nd(X) 7.79/3.11 a__from(X) -> from(X) 7.79/3.11 7.79/3.11 The set Q consists of the following terms: 7.79/3.11 7.79/3.11 a__from(x0) 7.79/3.11 mark(2nd(x0)) 7.79/3.11 mark(from(x0)) 7.79/3.11 mark(cons(x0, x1)) 7.79/3.11 mark(s(x0)) 7.79/3.11 a__2nd(x0) 7.79/3.11 7.79/3.11 7.79/3.11 ---------------------------------------- 7.79/3.11 7.79/3.11 (1) DependencyPairsProof (EQUIVALENT) 7.79/3.11 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 7.79/3.11 ---------------------------------------- 7.79/3.11 7.79/3.11 (2) 7.79/3.11 Obligation: 7.79/3.11 Q DP problem: 7.79/3.11 The TRS P consists of the following rules: 7.79/3.11 7.79/3.11 A__2ND(cons(X, cons(Y, Z))) -> MARK(Y) 7.79/3.11 A__FROM(X) -> MARK(X) 7.79/3.11 MARK(2nd(X)) -> A__2ND(mark(X)) 7.79/3.11 MARK(2nd(X)) -> MARK(X) 7.79/3.11 MARK(from(X)) -> A__FROM(mark(X)) 7.79/3.11 MARK(from(X)) -> MARK(X) 7.79/3.11 MARK(cons(X1, X2)) -> MARK(X1) 7.79/3.11 MARK(s(X)) -> MARK(X) 7.79/3.11 7.79/3.11 The TRS R consists of the following rules: 7.79/3.11 7.79/3.11 a__2nd(cons(X, cons(Y, Z))) -> mark(Y) 7.79/3.11 a__from(X) -> cons(mark(X), from(s(X))) 7.79/3.11 mark(2nd(X)) -> a__2nd(mark(X)) 7.79/3.11 mark(from(X)) -> a__from(mark(X)) 7.79/3.11 mark(cons(X1, X2)) -> cons(mark(X1), X2) 7.79/3.11 mark(s(X)) -> s(mark(X)) 7.79/3.11 a__2nd(X) -> 2nd(X) 7.79/3.11 a__from(X) -> from(X) 7.79/3.11 7.79/3.11 The set Q consists of the following terms: 7.79/3.11 7.79/3.11 a__from(x0) 7.79/3.11 mark(2nd(x0)) 7.79/3.11 mark(from(x0)) 7.79/3.11 mark(cons(x0, x1)) 7.79/3.11 mark(s(x0)) 7.79/3.11 a__2nd(x0) 7.79/3.11 7.79/3.11 We have to consider all minimal (P,Q,R)-chains. 7.79/3.11 ---------------------------------------- 7.79/3.11 7.79/3.11 (3) QDPOrderProof (EQUIVALENT) 7.79/3.11 We use the reduction pair processor [LPAR04,JAR06]. 7.79/3.11 7.79/3.11 7.79/3.11 The following pairs can be oriented strictly and are deleted. popout

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all output return to TRS_Innermost 2019-03-28 22.12