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TRS_Innermost 2019-03-28 22.12 pair #432271254
details
property
value
status
complete
benchmark
Ex1_2_Luc02c_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n018.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.13517 seconds
cpu usage
5.05197
user time
4.81888
system time
0.233091
max virtual memory
1.8408888E7
max residence set size
326556.0
stage attributes
key
value
starexec-result
YES
output
4.81/2.09 YES 4.81/2.10 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 4.81/2.10 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.81/2.10 4.81/2.10 4.81/2.10 Termination w.r.t. Q of the given QTRS could be proven: 4.81/2.10 4.81/2.10 (0) QTRS 4.81/2.10 (1) QTRSRRRProof [EQUIVALENT, 91 ms] 4.81/2.10 (2) QTRS 4.81/2.10 (3) QTRSRRRProof [EQUIVALENT, 26 ms] 4.81/2.10 (4) QTRS 4.81/2.10 (5) QTRSRRRProof [EQUIVALENT, 14 ms] 4.81/2.10 (6) QTRS 4.81/2.10 (7) QTRSRRRProof [EQUIVALENT, 0 ms] 4.81/2.10 (8) QTRS 4.81/2.10 (9) QTRSRRRProof [EQUIVALENT, 10 ms] 4.81/2.10 (10) QTRS 4.81/2.10 (11) QTRSRRRProof [EQUIVALENT, 0 ms] 4.81/2.10 (12) QTRS 4.81/2.10 (13) RisEmptyProof [EQUIVALENT, 0 ms] 4.81/2.10 (14) YES 4.81/2.10 4.81/2.10 4.81/2.10 ---------------------------------------- 4.81/2.10 4.81/2.10 (0) 4.81/2.10 Obligation: 4.81/2.10 Q restricted rewrite system: 4.81/2.10 The TRS R consists of the following rules: 4.81/2.10 4.81/2.10 active(2nd(cons(X, cons(Y, Z)))) -> mark(Y) 4.81/2.10 active(from(X)) -> mark(cons(X, from(s(X)))) 4.81/2.10 active(2nd(X)) -> 2nd(active(X)) 4.81/2.10 active(cons(X1, X2)) -> cons(active(X1), X2) 4.81/2.10 active(from(X)) -> from(active(X)) 4.81/2.10 active(s(X)) -> s(active(X)) 4.81/2.10 2nd(mark(X)) -> mark(2nd(X)) 4.81/2.10 cons(mark(X1), X2) -> mark(cons(X1, X2)) 4.81/2.10 from(mark(X)) -> mark(from(X)) 4.81/2.10 s(mark(X)) -> mark(s(X)) 4.81/2.10 proper(2nd(X)) -> 2nd(proper(X)) 4.81/2.10 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 4.81/2.10 proper(from(X)) -> from(proper(X)) 4.81/2.10 proper(s(X)) -> s(proper(X)) 4.81/2.10 2nd(ok(X)) -> ok(2nd(X)) 4.81/2.10 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 4.81/2.10 from(ok(X)) -> ok(from(X)) 4.81/2.10 s(ok(X)) -> ok(s(X)) 4.81/2.10 top(mark(X)) -> top(proper(X)) 4.81/2.10 top(ok(X)) -> top(active(X)) 4.81/2.10 4.81/2.10 The set Q consists of the following terms: 4.81/2.10 4.81/2.10 active(from(x0)) 4.81/2.10 active(2nd(x0)) 4.81/2.10 active(cons(x0, x1)) 4.81/2.10 active(s(x0)) 4.81/2.10 2nd(mark(x0)) 4.81/2.10 cons(mark(x0), x1) 4.81/2.10 from(mark(x0)) 4.81/2.10 s(mark(x0)) 4.81/2.10 proper(2nd(x0)) 4.81/2.10 proper(cons(x0, x1)) 4.81/2.10 proper(from(x0)) 4.81/2.10 proper(s(x0)) 4.81/2.10 2nd(ok(x0)) 4.81/2.10 cons(ok(x0), ok(x1)) 4.81/2.10 from(ok(x0)) 4.81/2.10 s(ok(x0)) 4.81/2.10 top(mark(x0)) 4.81/2.10 top(ok(x0)) 4.81/2.10 4.81/2.10 4.81/2.10 ---------------------------------------- 4.81/2.10 4.81/2.10 (1) QTRSRRRProof (EQUIVALENT) 4.81/2.10 Used ordering: 4.81/2.10 Polynomial interpretation [POLO]: 4.81/2.10 4.81/2.10 POL(2nd(x_1)) = 2*x_1 4.81/2.10 POL(active(x_1)) = 2*x_1 4.81/2.10 POL(cons(x_1, x_2)) = x_1 + x_2 4.81/2.10 POL(from(x_1)) = x_1 4.81/2.10 POL(mark(x_1)) = x_1 4.81/2.10 POL(ok(x_1)) = 1 + 2*x_1 4.81/2.10 POL(proper(x_1)) = x_1 4.81/2.10 POL(s(x_1)) = x_1 4.81/2.10 POL(top(x_1)) = 2*x_1 4.81/2.10 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 4.81/2.10 4.81/2.10 2nd(ok(X)) -> ok(2nd(X)) 4.81/2.10 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 4.81/2.10 top(ok(X)) -> top(active(X)) 4.81/2.10 4.81/2.10 4.81/2.10 4.81/2.10 4.81/2.10 ---------------------------------------- 4.81/2.10
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