details

property	value
status	complete
benchmark	17.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n020.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0762100219727 seconds
cpu usage	0.048031308
max memory	1630208.0

stage attributes

key	value
output-size	4101
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. !dot : [o * o] --> o 1 : [] --> o i : [o] --> o !dot(1, X) => X !dot(X, 1) => X !dot(i(X), X) => 1 !dot(X, i(X)) => 1 i(1) => 1 i(i(X)) => X !dot(i(X), !dot(X, Y)) => Y !dot(X, !dot(i(X), Y)) => Y !dot(!dot(X, Y), Z) => !dot(X, !dot(Y, Z)) i(!dot(X, Y)) => !dot(i(Y), i(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]): !dot(1, X) >? X !dot(X, 1) >? X !dot(i(X), X) >? 1 !dot(X, i(X)) >? 1 i(1) >? 1 i(i(X)) >? X !dot(i(X), !dot(X, Y)) >? Y !dot(X, !dot(i(X), Y)) >? Y !dot(!dot(X, Y), Z) >? !dot(X, !dot(Y, Z)) i(!dot(X, Y)) >? !dot(i(Y), i(X)) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: !dot = \y0y1.1 + y0 + y1 1 = 1 i = \y0.y0 Using this interpretation, the requirements translate to: [[!dot(1, _x0)]] = 2 + x0 > x0 = [[_x0]] [[!dot(_x0, 1)]] = 2 + x0 > x0 = [[_x0]] [[!dot(i(_x0), _x0)]] = 1 + 2x0 >= 1 = [[1]] [[!dot(_x0, i(_x0))]] = 1 + 2x0 >= 1 = [[1]] [[i(1)]] = 1 >= 1 = [[1]] [[i(i(_x0))]] = x0 >= x0 = [[_x0]] [[!dot(i(_x0), !dot(_x0, _x1))]] = 2 + x1 + 2x0 > x1 = [[_x1]] [[!dot(_x0, !dot(i(_x0), _x1))]] = 2 + x1 + 2x0 > x1 = [[_x1]] [[!dot(!dot(_x0, _x1), _x2)]] = 2 + x0 + x1 + x2 >= 2 + x0 + x1 + x2 = [[!dot(_x0, !dot(_x1, _x2))]] [[i(!dot(_x0, _x1))]] = 1 + x0 + x1 >= 1 + x0 + x1 = [[!dot(i(_x1), i(_x0))]] We can thus remove the following rules: !dot(1, X) => X !dot(X, 1) => X !dot(i(X), !dot(X, Y)) => Y !dot(X, !dot(i(X), Y)) => 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]): !dot(i(X), X) >? 1 !dot(X, i(X)) >? 1 i(1) >? 1 i(i(X)) >? X !dot(!dot(X, Y), Z) >? !dot(X, !dot(Y, Z)) i(!dot(X, Y)) >? !dot(i(Y), i(X)) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: !dot = \y0y1.1 + y0 + y1 1 = 0 i = \y0.2y0 Using this interpretation, the requirements translate to: [[!dot(i(_x0), _x0)]] = 1 + 3x0 > 0 = [[1]] [[!dot(_x0, i(_x0))]] = 1 + 3x0 > 0 = [[1]] [[i(1)]] = 0 >= 0 = [[1]] [[i(i(_x0))]] = 4x0 >= x0 = [[_x0]] [[!dot(!dot(_x0, _x1), _x2)]] = 2 + x0 + x1 + x2 >= 2 + x0 + x1 + x2 = [[!dot(_x0, !dot(_x1, _x2))]] [[i(!dot(_x0, _x1))]] = 2 + 2x0 + 2x1 > 1 + 2x0 + 2x1 = [[!dot(i(_x1), i(_x0))]] We can thus remove the following rules: !dot(i(X), X) => 1 popout

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actions

all output return to TRS Stand 20472