details

property	value
status	complete
benchmark	312.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n067.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.79265 seconds
cpu usage	10.3933
user time	9.93888
system time	0.454398
max virtual memory	1.8481776E7
max residence set size	887276.0

stage attributes

key	value
starexec-result	MAYBE

output

10.07/3.74 MAYBE 10.32/3.75 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.32/3.75 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.32/3.75 10.32/3.75 10.32/3.75 Quasi decreasingness of the given CTRS could not be shown: 10.32/3.75 10.32/3.75 (0) CTRS 10.32/3.75 (1) CTRSToQTRSProof [SOUND, 0 ms] 10.32/3.75 (2) QTRS 10.32/3.75 (3) QTRSRRRProof [EQUIVALENT, 71 ms] 10.32/3.75 (4) QTRS 10.32/3.75 (5) DependencyPairsProof [EQUIVALENT, 0 ms] 10.32/3.75 (6) QDP 10.32/3.75 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 10.32/3.75 (8) AND 10.32/3.75 (9) QDP 10.32/3.75 (10) UsableRulesProof [EQUIVALENT, 0 ms] 10.32/3.75 (11) QDP 10.32/3.75 (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] 10.32/3.75 (13) YES 10.32/3.75 (14) QDP 10.32/3.75 (15) UsableRulesProof [EQUIVALENT, 0 ms] 10.32/3.75 (16) QDP 10.32/3.75 (17) TransformationProof [EQUIVALENT, 0 ms] 10.32/3.75 (18) QDP 10.32/3.75 (19) TransformationProof [EQUIVALENT, 0 ms] 10.32/3.75 (20) QDP 10.32/3.75 (21) MRRProof [EQUIVALENT, 0 ms] 10.32/3.75 (22) QDP 10.32/3.75 (23) TransformationProof [EQUIVALENT, 0 ms] 10.32/3.75 (24) QDP 10.32/3.75 (25) NonTerminationLoopProof [COMPLETE, 0 ms] 10.32/3.75 (26) NO 10.32/3.75 10.32/3.75 10.32/3.75 ---------------------------------------- 10.32/3.75 10.32/3.75 (0) 10.32/3.75 Obligation: 10.32/3.75 Conditional term rewrite system: 10.32/3.75 The TRS R consists of the following rules: 10.32/3.75 10.32/3.75 gcd(x, 0) -> x 10.32/3.75 gcd(0, x) -> x 10.32/3.75 iadd(y) -> tp2(0, y) 10.32/3.75 iadd(s(z)) -> u1(iadd(z)) 10.32/3.75 u1(tp2(x, y)) -> tp2(s(x), y) 10.32/3.75 iadd(add(x, y)) -> tp2(x, y) 10.32/3.75 10.32/3.75 The conditional TRS C consists of the following conditional rules: 10.32/3.75 10.32/3.75 gcd(z, y) -> gcd(x, y) <= iadd(z) -> tp2(x, y) 10.32/3.75 gcd(y, z) -> gcd(x, y) <= iadd(z) -> tp2(x, y) 10.32/3.75 10.32/3.75 10.32/3.75 ---------------------------------------- 10.32/3.75 10.32/3.75 (1) CTRSToQTRSProof (SOUND) 10.32/3.75 The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. 10.32/3.75 ---------------------------------------- 10.32/3.75 10.32/3.75 (2) 10.32/3.75 Obligation: 10.32/3.75 Q restricted rewrite system: 10.32/3.75 The TRS R consists of the following rules: 10.32/3.75 10.32/3.75 gcd(z, y) -> U1(iadd(z), y) 10.32/3.75 U1(tp2(x, y), y) -> gcd(x, y) 10.32/3.75 gcd(y, z) -> U2(iadd(z), y) 10.32/3.75 U2(tp2(x, y), y) -> gcd(x, y) 10.32/3.75 gcd(x, 0) -> x 10.32/3.75 gcd(0, x) -> x 10.32/3.75 iadd(y) -> tp2(0, y) 10.32/3.75 iadd(s(z)) -> u1(iadd(z)) 10.32/3.75 u1(tp2(x, y)) -> tp2(s(x), y) 10.32/3.75 iadd(add(x, y)) -> tp2(x, y) 10.32/3.75 10.32/3.75 Q is empty. 10.32/3.75 10.32/3.75 ---------------------------------------- 10.32/3.75 10.32/3.75 (3) QTRSRRRProof (EQUIVALENT) 10.32/3.75 Used ordering: 10.32/3.75 Polynomial interpretation [POLO]: 10.32/3.75 10.32/3.75 POL(0) = 0 10.32/3.75 POL(U1(x_1, x_2)) = x_1 + x_2 10.32/3.75 POL(U2(x_1, x_2)) = x_1 + 2*x_2 10.32/3.75 POL(add(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 10.32/3.75 POL(gcd(x_1, x_2)) = 1 + 2*x_1 + x_2 10.32/3.75 POL(iadd(x_1)) = 1 + x_1 10.32/3.75 POL(s(x_1)) = x_1 10.32/3.75 POL(tp2(x_1, x_2)) = 1 + 2*x_1 + x_2 10.32/3.75 POL(u1(x_1)) = x_1 10.32/3.75 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 10.32/3.75 10.32/3.75 gcd(x, 0) -> x 10.32/3.75 gcd(0, x) -> x 10.32/3.75 iadd(add(x, y)) -> tp2(x, y) popout

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actions

all output return to TRS_Conditional 2019-03-28 22.59