details

property	value
status	complete
benchmark	#3.17_mset.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	INVY_15

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.0321 seconds
cpu usage	8.40009
user time	7.97053
system time	0.429567
max virtual memory	1.868254E7
max residence set size	887256.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 65 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 8 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 63 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 26 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 35 ms] (10) RelTRS (11) RelTRSRRRProof [EQUIVALENT, 14 ms] (12) RelTRS (13) RIsEmptyProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) The relative TRS consists of the following S rules: cons(x, cons(y, l)) -> cons(y, cons(x, l)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(0) = 0 POL(app(x_1, x_2)) = x_1 + x_2 POL(cons(x_1, x_2)) = 1 + x_1 + x_2 POL(nil) = 1 POL(plus(x_1, x_2)) = 1 + x_1 + x_2 POL(s(x_1)) = x_1 POL(sum(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: app(nil, k) -> k app(l, nil) -> l plus(0, y) -> y Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) plus(s(x), y) -> s(plus(x, y)) The relative TRS consists of the following S rules: cons(x, cons(y, l)) -> cons(y, cons(x, l)) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(app(x_1, x_2)) = x_1 + x_2 POL(cons(x_1, x_2)) = 1 + x_1 + x_2 POL(nil) = 0 POL(plus(x_1, x_2)) = x_1 + x_2 POL(s(x_1)) = x_1 POL(sum(x_1)) = x_1 popout

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job log

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actions

all output return to TRS Relative