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TRS Innermost pair #487524205
details
property
value
status
complete
benchmark
ExIntrod_GM01_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.74695396423 seconds
cpu usage
7.129403304
max memory
4.74099712E8
stage attributes
key
value
output-size
23784
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 69 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 13 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 11 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) DependencyPairsProof [EQUIVALENT, 0 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) QDP (13) MRRProof [EQUIVALENT, 22 ms] (14) QDP (15) MRRProof [EQUIVALENT, 40 ms] (16) QDP (17) MRRProof [EQUIVALENT, 0 ms] (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 47 ms] (22) QDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__incr(nil) -> nil a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L)) a__adx(nil) -> nil a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L))) a__nats -> a__adx(a__zeros) a__zeros -> cons(0, zeros) a__head(cons(X, L)) -> mark(X) a__tail(cons(X, L)) -> mark(L) mark(incr(X)) -> a__incr(mark(X)) mark(adx(X)) -> a__adx(mark(X)) mark(nats) -> a__nats mark(zeros) -> a__zeros mark(head(X)) -> a__head(mark(X)) mark(tail(X)) -> a__tail(mark(X)) mark(nil) -> nil mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__incr(X) -> incr(X) a__adx(X) -> adx(X) a__nats -> nats a__zeros -> zeros a__head(X) -> head(X) a__tail(X) -> tail(X) The set Q consists of the following terms: a__nats a__zeros mark(incr(x0)) mark(adx(x0)) mark(nats) mark(zeros) mark(head(x0)) mark(tail(x0)) mark(nil) mark(cons(x0, x1)) mark(s(x0)) mark(0) a__incr(x0) a__adx(x0) a__head(x0) a__tail(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(a__adx(x_1)) = x_1
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