details

property	value
status	complete
benchmark	Ex2_Luc03b.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.4106 seconds
cpu usage	3.34839
user time	3.19739
system time	0.150993
max virtual memory	1.8407092E7
max residence set size	217308.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 50 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 10 ms] (4) CSR (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: fst(0, Z) -> nil fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) from(X) -> cons(X, from(s(X))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) len(nil) -> 0 len(cons(X, Z)) -> s(len(Z)) The replacement map contains the following entries: fst: {1, 2} 0: empty set nil: empty set s: empty set cons: {1} from: {1} add: {1, 2} len: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: fst(0, Z) -> nil fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) from(X) -> cons(X, from(s(X))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) len(nil) -> 0 len(cons(X, Z)) -> s(len(Z)) The replacement map contains the following entries: fst: {1, 2} 0: empty set nil: empty set s: empty set cons: {1} from: {1} add: {1, 2} len: {1} Used ordering: Polynomial interpretation [POLO]: POL(0) = 1 POL(add(x_1, x_2)) = x_1 + x_2 POL(cons(x_1, x_2)) = 1 + x_1 POL(from(x_1)) = 1 + x_1 POL(fst(x_1, x_2)) = x_1 + x_2 POL(len(x_1)) = x_1 POL(nil) = 1 POL(s(x_1)) = 1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) add(0, X) -> X ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: fst(0, Z) -> nil from(X) -> cons(X, from(s(X))) add(s(X), Y) -> s(add(X, Y)) len(nil) -> 0 len(cons(X, Z)) -> s(len(Z)) The replacement map contains the following entries: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Contextsensitive