details

property	value
status	complete
benchmark	#3.6.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	NTI_23
configuration	default
runtime (wallclock)	55.566904068 seconds
cpu usage	200.292986495
max memory	1.4455345152E10

stage attributes

key	value
output-size	3672
starexec-result	"YES"

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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... ## 3 initial DP problems to solve. ## First, we try to decompose these problems into smaller problems. ## Round 1 [3 DP problems]: ## DP problem: Dependency pairs = [gcd^#(s(_0),s(_1)) -> if_gcd^#(le(_1,_0),s(_0),s(_1)), if_gcd^#(false,s(_0),s(_1)) -> gcd^#(minus(_1,_0),s(_0)), if_gcd^#(true,s(_0),s(_1)) -> gcd^#(minus(_0,_1),s(_1))] TRS = {le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), pred(s(_0)) -> _0, minus(_0,0) -> _0, minus(_0,s(_1)) -> pred(minus(_0,_1)), gcd(0,_0) -> _0, gcd(s(_0),0) -> s(_0), gcd(s(_0),s(_1)) -> if_gcd(le(_1,_0),s(_0),s(_1)), if_gcd(true,s(_0),s(_1)) -> gcd(minus(_0,_1),s(_1)), if_gcd(false,s(_0),s(_1)) -> gcd(minus(_1,_0),s(_0))} ## DP Processor: homeomorphic embeddings. Using no argument filtering, i.e., applying the processor to the full problem only. Failed! ## DP Processor: lexicographic path orders. Failed! ## DP Processor: polynomial interpretations. Using argument filtering: {gcd:[0, 1], minus:[0], pred:[0], if_gcd^#:[0, 1, 2], s:[0], gcd^#:[0, 1], if_gcd:[0, 1, 2], le:[0]}. Polynomial order induced by the interpretation: {gcd(_0,_1):[_0 + _1 * _0], true:[1], 0:[1], false:[1], le(_0):[_0], pred(_0):[_0], if_gcd^#(_0,_1,_2):[_0 * _1], minus(_0):[_0], s(_0):[1 + _0], gcd^#(_0,_1):[_0 * _1], if_gcd(_0,_1,_2):[_0 + _1 * _2]} and the value mu = 1 (see [Giesl, RTA'95]) Success, finiteness proved! This DP problem is finite. ## DP problem: Dependency pairs = [minus^#(_0,s(_1)) -> minus^#(_0,_1)] TRS = {le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), pred(s(_0)) -> _0, minus(_0,0) -> _0, minus(_0,s(_1)) -> pred(minus(_0,_1)), gcd(0,_0) -> _0, gcd(s(_0),0) -> s(_0), gcd(s(_0),s(_1)) -> if_gcd(le(_1,_0),s(_0),s(_1)), if_gcd(true,s(_0),s(_1)) -> gcd(minus(_0,_1),s(_1)), if_gcd(false,s(_0),s(_1)) -> gcd(minus(_1,_0),s(_0))} ## 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 = [le^#(s(_0),s(_1)) -> le^#(_0,_1)] TRS = {le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), pred(s(_0)) -> _0, minus(_0,0) -> _0, minus(_0,s(_1)) -> pred(minus(_0,_1)), gcd(0,_0) -> _0, gcd(s(_0),0) -> s(_0), gcd(s(_0),s(_1)) -> if_gcd(le(_1,_0),s(_0),s(_1)), if_gcd(true,s(_0),s(_1)) -> gcd(minus(_0,_1),s(_1)), if_gcd(false,s(_0),s(_1)) -> gcd(minus(_1,_0),s(_0))} ## 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. ## 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 = 1923594 popout

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actions

all output return to TRS Standard