details

property	value
status	complete
benchmark	aprove01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n059.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.20684 seconds
cpu usage	20.5786
user time	19.4446
system time	1.13394
max virtual memory	5.9006752E7
max residence set size	3347612.0

stage attributes

key	value
starexec-result	YES

output

20.20/6.11 YES 20.20/6.14 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 20.20/6.14 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.20/6.14 20.20/6.14 20.20/6.14 Termination w.r.t. Q of the given QTRS could be proven: 20.20/6.14 20.20/6.14 (0) QTRS 20.20/6.14 (1) DependencyPairsProof [EQUIVALENT, 34 ms] 20.20/6.14 (2) QDP 20.20/6.14 (3) DependencyGraphProof [EQUIVALENT, 8 ms] 20.20/6.14 (4) AND 20.20/6.14 (5) QDP 20.20/6.14 (6) MNOCProof [EQUIVALENT, 0 ms] 20.20/6.14 (7) QDP 20.20/6.14 (8) UsableRulesProof [EQUIVALENT, 0 ms] 20.20/6.14 (9) QDP 20.20/6.14 (10) QReductionProof [EQUIVALENT, 0 ms] 20.20/6.14 (11) QDP 20.20/6.14 (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.20/6.14 (13) YES 20.20/6.14 (14) QDP 20.20/6.14 (15) UsableRulesProof [EQUIVALENT, 0 ms] 20.20/6.14 (16) QDP 20.20/6.14 (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.20/6.14 (18) YES 20.20/6.14 (19) QDP 20.20/6.14 (20) MNOCProof [EQUIVALENT, 0 ms] 20.20/6.14 (21) QDP 20.20/6.14 (22) UsableRulesProof [EQUIVALENT, 0 ms] 20.20/6.14 (23) QDP 20.20/6.14 (24) QReductionProof [EQUIVALENT, 0 ms] 20.20/6.14 (25) QDP 20.20/6.14 (26) QDPOrderProof [EQUIVALENT, 36 ms] 20.20/6.14 (27) QDP 20.20/6.14 (28) QDPOrderProof [EQUIVALENT, 21 ms] 20.20/6.14 (29) QDP 20.20/6.14 (30) PisEmptyProof [EQUIVALENT, 0 ms] 20.20/6.14 (31) YES 20.20/6.14 (32) QDP 20.20/6.14 (33) MNOCProof [EQUIVALENT, 0 ms] 20.20/6.14 (34) QDP 20.20/6.14 (35) UsableRulesProof [EQUIVALENT, 0 ms] 20.20/6.14 (36) QDP 20.20/6.14 (37) QReductionProof [EQUIVALENT, 0 ms] 20.20/6.14 (38) QDP 20.20/6.14 (39) QDPOrderProof [EQUIVALENT, 23 ms] 20.20/6.14 (40) QDP 20.20/6.14 (41) DependencyGraphProof [EQUIVALENT, 0 ms] 20.20/6.14 (42) TRUE 20.20/6.14 20.20/6.14 20.20/6.14 ---------------------------------------- 20.20/6.14 20.20/6.14 (0) 20.20/6.14 Obligation: 20.20/6.14 Q restricted rewrite system: 20.20/6.14 The TRS R consists of the following rules: 20.20/6.14 20.20/6.14 p(0(x1)) -> 0(s(s(p(x1)))) 20.20/6.14 p(s(x1)) -> x1 20.20/6.14 p(p(s(x1))) -> p(x1) 20.20/6.14 f(s(x1)) -> p(s(g(p(s(s(x1)))))) 20.20/6.14 g(s(x1)) -> p(p(s(s(s(j(s(p(s(p(s(x1))))))))))) 20.20/6.14 j(s(x1)) -> p(s(s(p(s(f(p(s(p(p(s(x1))))))))))) 20.20/6.14 half(0(x1)) -> 0(s(s(half(p(s(p(s(x1)))))))) 20.20/6.14 half(s(s(x1))) -> s(half(p(p(s(s(x1)))))) 20.20/6.14 rd(0(x1)) -> 0(s(0(0(0(0(s(0(rd(x1))))))))) 20.20/6.14 20.20/6.14 Q is empty. 20.20/6.14 20.20/6.14 ---------------------------------------- 20.20/6.14 20.20/6.14 (1) DependencyPairsProof (EQUIVALENT) 20.20/6.14 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 20.20/6.14 ---------------------------------------- 20.20/6.14 20.20/6.14 (2) 20.20/6.14 Obligation: 20.20/6.14 Q DP problem: 20.20/6.14 The TRS P consists of the following rules: 20.20/6.14 20.20/6.14 P(0(x1)) -> P(x1) 20.20/6.14 P(p(s(x1))) -> P(x1) 20.20/6.14 F(s(x1)) -> P(s(g(p(s(s(x1)))))) 20.20/6.14 F(s(x1)) -> G(p(s(s(x1)))) 20.20/6.14 F(s(x1)) -> P(s(s(x1))) 20.20/6.14 G(s(x1)) -> P(p(s(s(s(j(s(p(s(p(s(x1))))))))))) 20.20/6.14 G(s(x1)) -> P(s(s(s(j(s(p(s(p(s(x1)))))))))) 20.20/6.14 G(s(x1)) -> J(s(p(s(p(s(x1)))))) 20.20/6.14 G(s(x1)) -> P(s(p(s(x1)))) 20.20/6.14 G(s(x1)) -> P(s(x1)) 20.20/6.14 J(s(x1)) -> P(s(s(p(s(f(p(s(p(p(s(x1))))))))))) 20.20/6.14 J(s(x1)) -> P(s(f(p(s(p(p(s(x1)))))))) 20.20/6.14 J(s(x1)) -> F(p(s(p(p(s(x1)))))) 20.20/6.14 J(s(x1)) -> P(s(p(p(s(x1))))) 20.20/6.14 J(s(x1)) -> P(p(s(x1))) 20.20/6.14 J(s(x1)) -> P(s(x1)) 20.20/6.14 HALF(0(x1)) -> HALF(p(s(p(s(x1))))) 20.20/6.14 HALF(0(x1)) -> P(s(p(s(x1)))) popout

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all output return to SRS_Standard 2019-03-29 03.29