details

property	value
status	complete
benchmark	#3.17a_mset.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	INVY_15

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.18196582794 seconds
cpu usage	9.232118951
max memory	1.07493376E9

stage attributes

key	value
output-size	10361
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 61 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 12 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 0 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 0 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 42 ms] (10) RelTRS (11) RelTRSRRRProof [EQUIVALENT, 13 ms] (12) RelTRS (13) RelTRSRRRProof [EQUIVALENT, 20 ms] (14) RelTRS (15) RelTRSRRRProof [EQUIVALENT, 13 ms] (16) RelTRS (17) RIsEmptyProof [EQUIVALENT, 0 ms] (18) 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)) sum(plus(cons(0, x), cons(y, l))) -> pred(sum(cons(s(x), cons(y, l)))) pred(cons(s(x), nil)) -> cons(x, nil) 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) = 1 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)) = 1 + x_1 + x_2 POL(pred(x_1)) = 1 + x_1 POL(s(x_1)) = 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: plus(0, y) -> y pred(cons(s(x), nil)) -> cons(x, nil) Rules from S: none ---------------------------------------- (2) 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(s(x), y) -> s(plus(x, y)) sum(plus(cons(0, x), cons(y, l))) -> pred(sum(cons(s(x), cons(y, l)))) The relative TRS consists of the following S rules: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Relative