Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Integ TRS Inner 43557 pair #381740642
details
property
value
status
complete
benchmark
A13.itrs
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n103.star.cs.uiowa.edu
space
Mixed_ITRS_2014
run statistics
property
value
solver
Ctrl
configuration
Itrs
runtime (wallclock)
0.478148937225 seconds
cpu usage
0.498933519
max memory
1.0510336E7
stage attributes
key
value
output-size
3626
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_Itrs /export/starexec/sandbox2/benchmark/theBenchmark.itrs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES DP problem for innermost termination. P = cond#(true, I0, I1, I2) -> d#(I0, I1 + 1, I1 + 1 + I2) dNat#(true, I3, I4, I5) -> cond#(I3 >= I5, I3, I4 - 1, I5) d#(I6, I7, I8) -> dNat#(I6 >= 0 && I7 >= 1 && I8 >= 0, I6, I7, I8) divNat#(true, I9, I10) -> d#(I9, I10, 0) div#(I11, I12) -> divNat#(I11 >= 0 && I12 >= 1, I11, I12) R = cond(false, x, y, z) -> 0 cond(true, I0, I1, I2) -> 1 + d(I0, I1 + 1, I1 + 1 + I2) dNat(true, I3, I4, I5) -> cond(I3 >= I5, I3, I4 - 1, I5) d(I6, I7, I8) -> dNat(I6 >= 0 && I7 >= 1 && I8 >= 0, I6, I7, I8) divNat(true, I9, I10) -> d(I9, I10, 0) div(I11, I12) -> divNat(I11 >= 0 && I12 >= 1, I11, I12) This problem is converted using chaining, where edges between chained DPs are removed. DP problem for innermost termination. P = cond#(true, I0, I1, I2) -> d#(I0, I1 + 1, I1 + 1 + I2) dNat#(true, I3, I4, I5) -> cond#(I3 >= I5, I3, I4 - 1, I5) d#(I6, I7, I8) -> dNat#(I6 >= 0 && I7 >= 1 && I8 >= 0, I6, I7, I8) divNat#(true, I9, I10) -> d#(I9, I10, 0) div#(I11, I12) -> divNat#(I11 >= 0 && I12 >= 1, I11, I12) div#(I11, I12) -> d#(I11, I12, 0) [I11 >= 0 && I12 >= 1] d#(I6, I7, I8) -> cond#(I6 >= I8, I6, I7 - 1, I8) [I6 >= 0 && I7 >= 1 && I8 >= 0] d#(I6, I7, I8) -> d#(I6, I7 - 1 + 1, I7 - 1 + 1 + I8) [I6 >= 0 && I7 >= 1 && I8 >= 0, I6 >= I8] dNat#(true, I3, I4, I5) -> d#(I3, I4 - 1 + 1, I4 - 1 + 1 + I5) [I3 >= I5] R = cond(false, x, y, z) -> 0 cond(true, I0, I1, I2) -> 1 + d(I0, I1 + 1, I1 + 1 + I2) dNat(true, I3, I4, I5) -> cond(I3 >= I5, I3, I4 - 1, I5) d(I6, I7, I8) -> dNat(I6 >= 0 && I7 >= 1 && I8 >= 0, I6, I7, I8) divNat(true, I9, I10) -> d(I9, I10, 0) div(I11, I12) -> divNat(I11 >= 0 && I12 >= 1, I11, I12) The dependency graph for this problem is: 0 -> 7, 6, 2 1 -> 2 -> 3 -> 7, 6, 2 4 -> 5 -> 7, 6, 2 6 -> 7 -> 7, 2, 6 8 -> 2, 6, 7 Where: 0) cond#(true, I0, I1, I2) -> d#(I0, I1 + 1, I1 + 1 + I2) 1) dNat#(true, I3, I4, I5) -> cond#(I3 >= I5, I3, I4 - 1, I5) 2) d#(I6, I7, I8) -> dNat#(I6 >= 0 && I7 >= 1 && I8 >= 0, I6, I7, I8) 3) divNat#(true, I9, I10) -> d#(I9, I10, 0) 4) div#(I11, I12) -> divNat#(I11 >= 0 && I12 >= 1, I11, I12) 5) div#(I11, I12) -> d#(I11, I12, 0) [I11 >= 0 && I12 >= 1] 6) d#(I6, I7, I8) -> cond#(I6 >= I8, I6, I7 - 1, I8) [I6 >= 0 && I7 >= 1 && I8 >= 0] 7) d#(I6, I7, I8) -> d#(I6, I7 - 1 + 1, I7 - 1 + 1 + I8) [I6 >= 0 && I7 >= 1 && I8 >= 0, I6 >= I8] 8) dNat#(true, I3, I4, I5) -> d#(I3, I4 - 1 + 1, I4 - 1 + 1 + I5) [I3 >= I5] We have the following SCCs. { 7 } DP problem for innermost termination. P = d#(I6, I7, I8) -> d#(I6, I7 - 1 + 1, I7 - 1 + 1 + I8) [I6 >= 0 && I7 >= 1 && I8 >= 0, I6 >= I8] R = cond(false, x, y, z) -> 0 cond(true, I0, I1, I2) -> 1 + d(I0, I1 + 1, I1 + 1 + I2) dNat(true, I3, I4, I5) -> cond(I3 >= I5, I3, I4 - 1, I5) d(I6, I7, I8) -> dNat(I6 >= 0 && I7 >= 1 && I8 >= 0, I6, I7, I8) divNat(true, I9, I10) -> d(I9, I10, 0) div(I11, I12) -> divNat(I11 >= 0 && I12 >= 1, I11, I12) We use the reverse value criterion with the projection function NU: NU[d#(z1,z2,z3)] = z1 + -1 * z3 This gives the following inequalities: I6 >= 0 && I7 >= 1 && I8 >= 0/\I6 >= I8 ==> I6 + -1 * I8 > I6 + -1 * (I7 - 1 + 1 + I8) with I6 + -1 * I8 >= 0 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Integ TRS Inner 43557