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	n080.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.38757 seconds
cpu usage	3.17331
user time	3.03409
system time	0.139224
max virtual memory	1.8275288E7
max residence set size	202792.0

stage attributes

key	value
starexec-result	YES

output

2.86/1.34 YES 2.86/1.35 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.86/1.35 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.86/1.35 2.86/1.35 2.86/1.35 Termination of the given CSR could be proven: 2.86/1.35 2.86/1.35 (0) CSR 2.86/1.35 (1) CSRRRRProof [EQUIVALENT, 63 ms] 2.86/1.35 (2) CSR 2.86/1.35 (3) RisEmptyProof [EQUIVALENT, 0 ms] 2.86/1.35 (4) YES 2.86/1.35 2.86/1.35 2.86/1.35 ---------------------------------------- 2.86/1.35 2.86/1.35 (0) 2.86/1.35 Obligation: 2.86/1.35 Context-sensitive rewrite system: 2.86/1.35 The TRS R consists of the following rules: 2.86/1.35 2.86/1.35 fst(0, Z) -> nil 2.86/1.35 fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) 2.86/1.35 from(X) -> cons(X, from(s(X))) 2.86/1.35 add(0, X) -> X 2.86/1.35 add(s(X), Y) -> s(add(X, Y)) 2.86/1.35 len(nil) -> 0 2.86/1.35 len(cons(X, Z)) -> s(len(Z)) 2.86/1.35 2.86/1.35 The replacement map contains the following entries: 2.86/1.35 2.86/1.35 fst: {1, 2} 2.86/1.35 0: empty set 2.86/1.35 nil: empty set 2.86/1.35 s: empty set 2.86/1.35 cons: {1} 2.86/1.35 from: {1} 2.86/1.35 add: {1, 2} 2.86/1.35 len: {1} 2.86/1.35 2.86/1.35 ---------------------------------------- 2.86/1.35 2.86/1.35 (1) CSRRRRProof (EQUIVALENT) 2.86/1.35 The following CSR is given: Context-sensitive rewrite system: 2.86/1.35 The TRS R consists of the following rules: 2.86/1.35 2.86/1.35 fst(0, Z) -> nil 2.86/1.35 fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) 2.86/1.35 from(X) -> cons(X, from(s(X))) 2.86/1.35 add(0, X) -> X 2.86/1.35 add(s(X), Y) -> s(add(X, Y)) 2.86/1.35 len(nil) -> 0 2.86/1.35 len(cons(X, Z)) -> s(len(Z)) 2.86/1.35 2.86/1.35 The replacement map contains the following entries: 2.86/1.35 2.86/1.35 fst: {1, 2} 2.86/1.35 0: empty set 2.86/1.35 nil: empty set 2.86/1.35 s: empty set 2.86/1.35 cons: {1} 2.86/1.35 from: {1} 2.86/1.35 add: {1, 2} 2.86/1.35 len: {1} 2.86/1.35 Used ordering: 2.86/1.35 Polynomial interpretation [POLO]: 2.86/1.35 2.86/1.35 POL(0) = 2 2.86/1.35 POL(add(x_1, x_2)) = 1 + x_1 + 2*x_2 2.86/1.35 POL(cons(x_1, x_2)) = 1 + 2*x_1 2.86/1.35 POL(from(x_1)) = 2 + 2*x_1 2.86/1.35 POL(fst(x_1, x_2)) = 2*x_1 + 2*x_2 2.86/1.35 POL(len(x_1)) = 2 + x_1 2.86/1.35 POL(nil) = 2 2.86/1.35 POL(s(x_1)) = 0 2.86/1.35 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 2.86/1.35 2.86/1.35 fst(0, Z) -> nil 2.86/1.35 fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) 2.86/1.35 from(X) -> cons(X, from(s(X))) 2.86/1.35 add(0, X) -> X 2.86/1.35 add(s(X), Y) -> s(add(X, Y)) 2.86/1.35 len(nil) -> 0 2.86/1.35 len(cons(X, Z)) -> s(len(Z)) 2.86/1.35 2.86/1.35 2.86/1.35 2.86/1.35 2.86/1.35 ---------------------------------------- 2.86/1.35 2.86/1.35 (2) 2.86/1.35 Obligation: 2.86/1.35 Context-sensitive rewrite system: 2.86/1.35 R is empty. 2.86/1.35 2.86/1.35 ---------------------------------------- 2.86/1.35 2.86/1.35 (3) RisEmptyProof (EQUIVALENT) 2.86/1.35 The CSR R is empty. Hence, termination is trivially proven. 2.86/1.35 ---------------------------------------- popout

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all output return to TRS_Contextsensitive 2019-03-21 05.07