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TRS Stand 20472 pair #381714708
details
property
value
status
complete
benchmark
Ex15_Luc98_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n002.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.77758097649 seconds
cpu usage
4.238857204
max memory
2.16559616E8
stage attributes
key
value
output-size
5334
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 70 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 15 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__and(true, X) -> mark(X) a__and(false, Y) -> false a__if(true, X, Y) -> mark(X) a__if(false, X, Y) -> mark(Y) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(add(X, Y)) a__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) a__from(X) -> cons(X, from(s(X))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) mark(add(X1, X2)) -> a__add(mark(X1), X2) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(from(X)) -> a__from(X) mark(true) -> true mark(false) -> false mark(0) -> 0 mark(s(X)) -> s(X) mark(nil) -> nil mark(cons(X1, X2)) -> cons(X1, X2) a__and(X1, X2) -> and(X1, X2) a__if(X1, X2, X3) -> if(X1, X2, X3) a__add(X1, X2) -> add(X1, X2) a__first(X1, X2) -> first(X1, X2) a__from(X) -> from(X) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 1 POL(a__add(x_1, x_2)) = 2 + x_1 + 2*x_2 POL(a__and(x_1, x_2)) = 2 + x_1 + 2*x_2 POL(a__first(x_1, x_2)) = 2 + x_1 + 2*x_2 POL(a__from(x_1)) = 2 + 2*x_1 POL(a__if(x_1, x_2, x_3)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 POL(add(x_1, x_2)) = 1 + x_1 + 2*x_2 POL(and(x_1, x_2)) = 1 + x_1 + 2*x_2 POL(cons(x_1, x_2)) = 1 + x_1 + x_2 POL(false) = 1 POL(first(x_1, x_2)) = 1 + x_1 + 2*x_2 POL(from(x_1)) = 1 + x_1 POL(if(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + 2*x_3 POL(mark(x_1)) = 2*x_1 POL(nil) = 1 POL(s(x_1)) = x_1 POL(true) = 1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__and(true, X) -> mark(X) a__and(false, Y) -> false a__if(true, X, Y) -> mark(X) a__if(false, X, Y) -> mark(Y) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(add(X, Y)) a__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) mark(true) -> true mark(false) -> false mark(0) -> 0 mark(nil) -> nil mark(cons(X1, X2)) -> cons(X1, X2) a__and(X1, X2) -> and(X1, X2) a__if(X1, X2, X3) -> if(X1, X2, X3) a__add(X1, X2) -> add(X1, X2)
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