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TRS Stand 20472 pair #381710806
details
property
value
status
complete
benchmark
filliatre.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n095.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.94641304016 seconds
cpu usage
4.812644042
max memory
3.08432896E8
stage attributes
key
value
output-size
6459
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 71 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 20 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 16 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 2 ms] (10) QTRS (11) RisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(A) -> A g(B) -> A g(B) -> B g(C) -> A g(C) -> B g(C) -> C foldf(x, nil) -> x foldf(x, cons(y, z)) -> f(foldf(x, z), y) f(t, x) -> f'(t, g(x)) f'(triple(a, b, c), C) -> triple(a, b, cons(C, c)) f'(triple(a, b, c), B) -> f(triple(a, b, c), A) f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b)) f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(A) = 0 POL(B) = 0 POL(C) = 2 POL(cons(x_1, x_2)) = x_1 + x_2 POL(f(x_1, x_2)) = x_1 + x_2 POL(f'(x_1, x_2)) = x_1 + x_2 POL(f''(x_1)) = x_1 POL(foldf(x_1, x_2)) = x_1 + x_2 POL(g(x_1)) = x_1 POL(nil) = 0 POL(triple(x_1, x_2, x_3)) = 2*x_1 + x_2 + x_3 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(C) -> A g(C) -> B ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(A) -> A g(B) -> A g(B) -> B g(C) -> C foldf(x, nil) -> x foldf(x, cons(y, z)) -> f(foldf(x, z), y) f(t, x) -> f'(t, g(x)) f'(triple(a, b, c), C) -> triple(a, b, cons(C, c)) f'(triple(a, b, c), B) -> f(triple(a, b, c), A) f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b)) f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT)
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