details

property	value
status	complete
benchmark	list-sum-prod-assoc.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n162.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	NTI_23
configuration	default
runtime (wallclock)	0.226738929749 seconds
cpu usage	0.329061618
max memory	3.8854656E7

stage attributes

key	value
output-size	4155
starexec-result	"YES"

output

/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES ** BEGIN proof argument ** All the DP problems were proved finite. As all the involved DP processors are sound, the TRS under analysis terminates. ** END proof argument ** ** BEGIN proof description ** ## Searching for a generalized rewrite rule (a rule whose right-hand side contains a variable that does not occur in the left-hand side)... No generalized rewrite rule found! ## Applying the DP framework... ## 4 initial DP problems to solve. ## First, we try to decompose these problems into smaller problems. ## Round 1 [4 DP problems]: ## DP problem: Dependency pairs = [prod^#(cons(_0,_1)) -> prod^#(_1)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), +(+(_0,_1),_2) -> +(_0,+(_1,_2)), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), *(*(_0,_1),_2) -> *(_0,*(_1,_2)), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1))} ## DP Processor: homeomorphic embeddings. Using no argument filtering, i.e., applying the processor to the full problem only. Success, finiteness proved! This DP problem is finite. ## DP problem: Dependency pairs = [sum^#(cons(_0,_1)) -> sum^#(_1)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), +(+(_0,_1),_2) -> +(_0,+(_1,_2)), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), *(*(_0,_1),_2) -> *(_0,*(_1,_2)), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1))} ## DP Processor: homeomorphic embeddings. Using no argument filtering, i.e., applying the processor to the full problem only. Success, finiteness proved! This DP problem is finite. ## DP problem: Dependency pairs = [*^#(s(_0),s(_1)) -> *^#(_0,_1), *^#(*(_0,_1),_2) -> *^#(_0,*(_1,_2)), *^#(*(_0,_1),_2) -> *^#(_1,_2)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), +(+(_0,_1),_2) -> +(_0,+(_1,_2)), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), *(*(_0,_1),_2) -> *(_0,*(_1,_2)), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1))} ## DP Processor: homeomorphic embeddings. Using no argument filtering, i.e., applying the processor to the full problem only. Failed! ## DP Processor: lexicographic path orders. Using no argument filtering, i.e., applying the processor to the full problem only. Lexicographic path order induced by the precedence: nil > [s, 0], * > [s, +], *^# > [s, *, +], cons > [prod, s, sum, *, +], + > [s] Success, finiteness proved! This DP problem is finite. ## DP problem: Dependency pairs = [+^#(s(_0),s(_1)) -> +^#(_0,_1), +^#(+(_0,_1),_2) -> +^#(_0,+(_1,_2)), +^#(+(_0,_1),_2) -> +^#(_1,_2)] TRS = {+(_0,0) -> _0, +(0,_0) -> _0, +(s(_0),s(_1)) -> s(s(+(_0,_1))), +(+(_0,_1),_2) -> +(_0,+(_1,_2)), *(_0,0) -> 0, *(0,_0) -> 0, *(s(_0),s(_1)) -> s(+(*(_0,_1),+(_0,_1))), *(*(_0,_1),_2) -> *(_0,*(_1,_2)), sum(nil) -> 0, sum(cons(_0,_1)) -> +(_0,sum(_1)), prod(nil) -> s(0), prod(cons(_0,_1)) -> *(_0,prod(_1))} ## DP Processor: homeomorphic embeddings. Using no argument filtering, i.e., applying the processor to the full problem only. Failed! ## DP Processor: lexicographic path orders. Using no argument filtering, i.e., applying the processor to the full problem only. Lexicographic path order induced by the precedence: nil > [s, 0], * > [s, +], +^# > [s, +], cons > [prod, s, sum, *, +], + > [s] Success, finiteness proved! This DP problem is finite. ## All the DP problems were proved finite. As all the involved DP processors are sound, the TRS under analysis terminates. Proof run on Linux version 3.10.0-1160.62.1.el7.x86_64 for amd64 using Java version 1.8.0_322 ** END proof description ** Total number of generated unfolded rules = 0 popout

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job log

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actions

all output return to TRS Standard