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TRS Stand 20472 pair #381716120
details
property
value
status
complete
benchmark
PEANO_nosorts_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n021.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.269404172897 seconds
cpu usage
0.209768464
max memory
4526080.0
stage attributes
key
value
output-size
15848
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o U11 : [o * o * o] --> o U12 : [o * o * o] --> o a!6220!6220U11 : [o * o * o] --> o a!6220!6220U12 : [o * o * o] --> o a!6220!6220plus : [o * o] --> o mark : [o] --> o plus : [o * o] --> o s : [o] --> o tt : [] --> o a!6220!6220U11(tt, X, Y) => a!6220!6220U12(tt, X, Y) a!6220!6220U12(tt, X, Y) => s(a!6220!6220plus(mark(Y), mark(X))) a!6220!6220plus(X, 0) => mark(X) a!6220!6220plus(X, s(Y)) => a!6220!6220U11(tt, Y, X) mark(U11(X, Y, Z)) => a!6220!6220U11(mark(X), Y, Z) mark(U12(X, Y, Z)) => a!6220!6220U12(mark(X), Y, Z) mark(plus(X, Y)) => a!6220!6220plus(mark(X), mark(Y)) mark(tt) => tt mark(s(X)) => s(mark(X)) mark(0) => 0 a!6220!6220U11(X, Y, Z) => U11(X, Y, Z) a!6220!6220U12(X, Y, Z) => U12(X, Y, Z) a!6220!6220plus(X, Y) => plus(X, Y) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): a!6220!6220U11(tt, X, Y) >? a!6220!6220U12(tt, X, Y) a!6220!6220U12(tt, X, Y) >? s(a!6220!6220plus(mark(Y), mark(X))) a!6220!6220plus(X, 0) >? mark(X) a!6220!6220plus(X, s(Y)) >? a!6220!6220U11(tt, Y, X) mark(U11(X, Y, Z)) >? a!6220!6220U11(mark(X), Y, Z) mark(U12(X, Y, Z)) >? a!6220!6220U12(mark(X), Y, Z) mark(plus(X, Y)) >? a!6220!6220plus(mark(X), mark(Y)) mark(tt) >? tt mark(s(X)) >? s(mark(X)) mark(0) >? 0 a!6220!6220U11(X, Y, Z) >? U11(X, Y, Z) a!6220!6220U12(X, Y, Z) >? U12(X, Y, Z) a!6220!6220plus(X, Y) >? plus(X, Y) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: 0 = 1 U11 = \y0y1y2.y0 + y2 + 2y1 U12 = \y0y1y2.y2 + 2y0 + 2y1 a!6220!6220U11 = \y0y1y2.y0 + y2 + 2y1 a!6220!6220U12 = \y0y1y2.y2 + 2y0 + 2y1 a!6220!6220plus = \y0y1.y0 + 2y1 mark = \y0.y0 plus = \y0y1.y0 + 2y1 s = \y0.y0 tt = 0 Using this interpretation, the requirements translate to: [[a!6220!6220U11(tt, _x0, _x1)]] = x1 + 2x0 >= x1 + 2x0 = [[a!6220!6220U12(tt, _x0, _x1)]] [[a!6220!6220U12(tt, _x0, _x1)]] = x1 + 2x0 >= x1 + 2x0 = [[s(a!6220!6220plus(mark(_x1), mark(_x0)))]] [[a!6220!6220plus(_x0, 0)]] = 2 + x0 > x0 = [[mark(_x0)]] [[a!6220!6220plus(_x0, s(_x1))]] = x0 + 2x1 >= x0 + 2x1 = [[a!6220!6220U11(tt, _x1, _x0)]] [[mark(U11(_x0, _x1, _x2))]] = x0 + x2 + 2x1 >= x0 + x2 + 2x1 = [[a!6220!6220U11(mark(_x0), _x1, _x2)]] [[mark(U12(_x0, _x1, _x2))]] = x2 + 2x0 + 2x1 >= x2 + 2x0 + 2x1 = [[a!6220!6220U12(mark(_x0), _x1, _x2)]] [[mark(plus(_x0, _x1))]] = x0 + 2x1 >= x0 + 2x1 = [[a!6220!6220plus(mark(_x0), mark(_x1))]] [[mark(tt)]] = 0 >= 0 = [[tt]] [[mark(s(_x0))]] = x0 >= x0 = [[s(mark(_x0))]] [[mark(0)]] = 1 >= 1 = [[0]] [[a!6220!6220U11(_x0, _x1, _x2)]] = x0 + x2 + 2x1 >= x0 + x2 + 2x1 = [[U11(_x0, _x1, _x2)]] [[a!6220!6220U12(_x0, _x1, _x2)]] = x2 + 2x0 + 2x1 >= x2 + 2x0 + 2x1 = [[U12(_x0, _x1, _x2)]] [[a!6220!6220plus(_x0, _x1)]] = x0 + 2x1 >= x0 + 2x1 = [[plus(_x0, _x1)]] We can thus remove the following rules: a!6220!6220plus(X, 0) => mark(X) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): a!6220!6220U11(tt, X, Y) >? a!6220!6220U12(tt, X, Y) a!6220!6220U12(tt, X, Y) >? s(a!6220!6220plus(mark(Y), mark(X))) a!6220!6220plus(X, s(Y)) >? a!6220!6220U11(tt, Y, X) mark(U11(X, Y, Z)) >? a!6220!6220U11(mark(X), Y, Z) mark(U12(X, Y, Z)) >? a!6220!6220U12(mark(X), Y, Z) mark(plus(X, Y)) >? a!6220!6220plus(mark(X), mark(Y)) mark(tt) >? tt
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