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TRS_Conditional 2019-03-28 22.59 pair #432272525
details
property
value
status
complete
benchmark
321.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.90659 seconds
cpu usage
4.35702
user time
4.16132
system time
0.195702
max virtual memory
1.8408888E7
max residence set size
282168.0
stage attributes
key
value
starexec-result
YES
output
4.18/1.86 YES 4.18/1.87 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 4.18/1.87 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.18/1.87 4.18/1.87 4.18/1.87 Quasi decreasingness of the given CTRS could be proven: 4.18/1.87 4.18/1.87 (0) CTRS 4.18/1.87 (1) CTRSToQTRSProof [SOUND, 0 ms] 4.18/1.87 (2) QTRS 4.18/1.87 (3) QTRSRRRProof [EQUIVALENT, 51 ms] 4.18/1.87 (4) QTRS 4.18/1.87 (5) QTRSRRRProof [EQUIVALENT, 0 ms] 4.18/1.87 (6) QTRS 4.18/1.87 (7) QTRSRRRProof [EQUIVALENT, 8 ms] 4.18/1.87 (8) QTRS 4.18/1.87 (9) QTRSRRRProof [EQUIVALENT, 0 ms] 4.18/1.87 (10) QTRS 4.18/1.87 (11) QTRSRRRProof [EQUIVALENT, 0 ms] 4.18/1.87 (12) QTRS 4.18/1.87 (13) QTRSRRRProof [EQUIVALENT, 1 ms] 4.18/1.87 (14) QTRS 4.18/1.87 (15) QTRSRRRProof [EQUIVALENT, 0 ms] 4.18/1.87 (16) QTRS 4.18/1.87 (17) RisEmptyProof [EQUIVALENT, 0 ms] 4.18/1.87 (18) YES 4.18/1.87 4.18/1.87 4.18/1.87 ---------------------------------------- 4.18/1.87 4.18/1.87 (0) 4.18/1.87 Obligation: 4.18/1.87 Conditional term rewrite system: 4.18/1.87 The TRS R consists of the following rules: 4.18/1.87 4.18/1.87 a -> c 4.18/1.87 a -> d 4.18/1.87 b -> c 4.18/1.87 b -> d 4.18/1.87 c -> e 4.18/1.87 c -> l 4.18/1.87 k -> l 4.18/1.87 k -> m 4.18/1.87 d -> m 4.18/1.87 4.18/1.87 The conditional TRS C consists of the following conditional rules: 4.18/1.87 4.18/1.87 f(x) -> x <= x -> e 4.18/1.87 g(d, x, y) -> A <= y -> x 4.18/1.87 h(x, y) -> g(x, y, f(k)) <= y -> x 4.18/1.87 4.18/1.87 4.18/1.87 ---------------------------------------- 4.18/1.87 4.18/1.87 (1) CTRSToQTRSProof (SOUND) 4.18/1.87 The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. 4.18/1.87 ---------------------------------------- 4.18/1.87 4.18/1.87 (2) 4.18/1.87 Obligation: 4.18/1.87 Q restricted rewrite system: 4.18/1.87 The TRS R consists of the following rules: 4.18/1.87 4.18/1.87 f(x) -> U1(x, x) 4.18/1.87 U1(e, x) -> x 4.18/1.87 g(d, x, y) -> U2(y) 4.18/1.87 U2(x) -> A 4.18/1.87 h(x, y) -> U3(y, x, y) 4.18/1.87 U3(x, x, y) -> g(x, y, f(k)) 4.18/1.87 a -> c 4.18/1.87 a -> d 4.18/1.87 b -> c 4.18/1.87 b -> d 4.18/1.87 c -> e 4.18/1.87 c -> l 4.18/1.87 k -> l 4.18/1.87 k -> m 4.18/1.87 d -> m 4.18/1.87 4.18/1.87 Q is empty. 4.18/1.87 4.18/1.87 ---------------------------------------- 4.18/1.87 4.18/1.87 (3) QTRSRRRProof (EQUIVALENT) 4.18/1.87 Used ordering: 4.18/1.87 Polynomial interpretation [POLO]: 4.18/1.87 4.18/1.87 POL(A) = 0 4.18/1.87 POL(U1(x_1, x_2)) = x_1 + x_2 4.18/1.87 POL(U2(x_1)) = 1 + x_1 4.18/1.87 POL(U3(x_1, x_2, x_3)) = 2 + x_1 + 2*x_2 + x_3 4.18/1.87 POL(a) = 2 4.18/1.87 POL(b) = 2 4.18/1.87 POL(c) = 0 4.18/1.87 POL(d) = 1 4.18/1.87 POL(e) = 0 4.18/1.87 POL(f(x_1)) = 2*x_1 4.18/1.87 POL(g(x_1, x_2, x_3)) = 2*x_1 + x_2 + x_3 4.18/1.87 POL(h(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 4.18/1.87 POL(k) = 1
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