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TRS Standard pair #487071438
details
property
value
status
complete
benchmark
Ex4_7_15_Bor03_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.83287 seconds
cpu usage
4.27371
user time
4.05434
system time
0.219376
max virtual memory
1.8478552E7
max residence set size
287404.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 58 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 9 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 0 ms] (10) QTRS (11) AAECC Innermost [EQUIVALENT, 0 ms] (12) QTRS (13) DependencyPairsProof [EQUIVALENT, 0 ms] (14) QDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(0) -> cons(0, f(s(0))) a__f(s(0)) -> a__f(a__p(s(0))) a__p(s(0)) -> 0 mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(0) -> 0 mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(a__f(x_1)) = 2 + 2*x_1 POL(a__p(x_1)) = 2*x_1 POL(cons(x_1, x_2)) = x_1 + x_2 POL(f(x_1)) = 1 + 2*x_1 POL(mark(x_1)) = 2*x_1 POL(p(x_1)) = 2*x_1 POL(s(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__f(0) -> cons(0, f(s(0))) a__f(X) -> f(X) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(s(0)) -> a__f(a__p(s(0))) a__p(s(0)) -> 0 mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(0) -> 0 mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) a__p(X) -> p(X) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(a__f(x_1)) = 1 + x_1
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