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TRS Innermost pair #487093459
details
property
value
status
complete
benchmark
ExIntrod_GM04_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.25991 seconds
cpu usage
5.10764
user time
4.86568
system time
0.241961
max virtual memory
1.8474676E7
max residence set size
324724.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 88 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 12 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 4 ms] (10) QTRS (11) QTRSRRRProof [EQUIVALENT, 5 ms] (12) QTRS (13) QTRSRRRProof [EQUIVALENT, 0 ms] (14) QTRS (15) RisEmptyProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__nats -> a__adx(a__zeros) a__zeros -> cons(0, zeros) a__incr(cons(X, Y)) -> cons(s(X), incr(Y)) a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y))) a__hd(cons(X, Y)) -> mark(X) a__tl(cons(X, Y)) -> mark(Y) mark(nats) -> a__nats mark(adx(X)) -> a__adx(mark(X)) mark(zeros) -> a__zeros mark(incr(X)) -> a__incr(mark(X)) mark(hd(X)) -> a__hd(mark(X)) mark(tl(X)) -> a__tl(mark(X)) mark(cons(X1, X2)) -> cons(X1, X2) mark(0) -> 0 mark(s(X)) -> s(X) a__nats -> nats a__adx(X) -> adx(X) a__zeros -> zeros a__incr(X) -> incr(X) a__hd(X) -> hd(X) a__tl(X) -> tl(X) The set Q consists of the following terms: a__nats a__zeros mark(nats) mark(adx(x0)) mark(zeros) mark(incr(x0)) mark(hd(x0)) mark(tl(x0)) mark(cons(x0, x1)) mark(0) mark(s(x0)) a__adx(x0) a__incr(x0) a__hd(x0) a__tl(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(a__adx(x_1)) = x_1 POL(a__hd(x_1)) = 1 + 2*x_1 POL(a__incr(x_1)) = x_1 POL(a__nats) = 0 POL(a__tl(x_1)) = 1 + 2*x_1 POL(a__zeros) = 0 POL(adx(x_1)) = x_1 POL(cons(x_1, x_2)) = x_1 + 2*x_2 POL(hd(x_1)) = 1 + 2*x_1 POL(incr(x_1)) = x_1 POL(mark(x_1)) = 2*x_1 POL(nats) = 0 POL(s(x_1)) = x_1 POL(tl(x_1)) = 1 + 2*x_1 POL(zeros) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__hd(cons(X, Y)) -> mark(X) a__tl(cons(X, Y)) -> mark(Y)
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