details

property	value
status	complete
benchmark	Ex2_Luc03b_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n100.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.81941008568 seconds
cpu usage	4.423227605
max memory	2.72781312E8

stage attributes

key	value
output-size	6273
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 65 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 12 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 7 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 0 ms] (10) QTRS (11) RisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: fst(0, Z) -> nil fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z))) from(X) -> cons(X, n__from(s(X))) add(0, X) -> X add(s(X), Y) -> s(n__add(activate(X), Y)) len(nil) -> 0 len(cons(X, Z)) -> s(n__len(activate(Z))) fst(X1, X2) -> n__fst(X1, X2) from(X) -> n__from(X) add(X1, X2) -> n__add(X1, X2) len(X) -> n__len(X) activate(n__fst(X1, X2)) -> fst(X1, X2) activate(n__from(X)) -> from(X) activate(n__add(X1, X2)) -> add(X1, X2) activate(n__len(X)) -> len(X) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(activate(x_1)) = 2 + 2*x_1 POL(add(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 POL(cons(x_1, x_2)) = 1 + x_1 + x_2 POL(from(x_1)) = 2 + 2*x_1 POL(fst(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 POL(len(x_1)) = 1 + 2*x_1 POL(n__add(x_1, x_2)) = x_1 + 2*x_2 POL(n__from(x_1)) = x_1 POL(n__fst(x_1, x_2)) = x_1 + x_2 POL(n__len(x_1)) = x_1 POL(nil) = 0 POL(s(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: fst(0, Z) -> nil fst(s(X), cons(Y, Z)) -> cons(Y, n__fst(activate(X), activate(Z))) add(0, X) -> X len(nil) -> 0 fst(X1, X2) -> n__fst(X1, X2) from(X) -> n__from(X) add(X1, X2) -> n__add(X1, X2) len(X) -> n__len(X) activate(n__add(X1, X2)) -> add(X1, X2) activate(n__len(X)) -> len(X) activate(X) -> X ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: from(X) -> cons(X, n__from(s(X))) add(s(X), Y) -> s(n__add(activate(X), Y)) len(cons(X, Z)) -> s(n__len(activate(Z))) popout

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actions

all output return to TRS Stand 20472