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TRS Standard pair #516960895
details
property
value
status
complete
benchmark
thiemann08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n116.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.76692295074 seconds
cpu usage
7.431597871
max memory
5.1871744E8
stage attributes
key
value
output-size
12938
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPOrderProof [EQUIVALENT, 59 ms] (13) QDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 35 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: empty(nil) -> true empty(cons(x, l)) -> false head(cons(x, l)) -> x tail(nil) -> nil tail(cons(x, l)) -> l rev(nil) -> nil rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l)) last(x, l) -> if(empty(l), x, l) if(true, x, l) -> x if(false, x, l) -> last(head(l), tail(l)) rev2(x, nil) -> nil rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: empty(nil) -> true empty(cons(x, l)) -> false head(cons(x, l)) -> x tail(nil) -> nil tail(cons(x, l)) -> l rev(nil) -> nil rev(cons(x, l)) -> cons(rev1(x, l), rev2(x, l)) last(x, l) -> if(empty(l), x, l) if(true, x, l) -> x if(false, x, l) -> last(head(l), tail(l)) rev2(x, nil) -> nil rev2(x, cons(y, l)) -> rev(cons(x, rev2(y, l))) The set Q consists of the following terms: empty(nil) empty(cons(x0, x1)) head(cons(x0, x1)) tail(nil) tail(cons(x0, x1)) rev(nil) rev(cons(x0, x1)) last(x0, x1) if(true, x0, x1) if(false, x0, x1) rev2(x0, nil) rev2(x0, cons(x1, x2))
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