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TRS Conte Sensi 17651 pair #381733256
details
property
value
status
complete
benchmark
ex5.5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n014.star.cs.uiowa.edu
space
Transformed_outermost_08
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.47937512398 seconds
cpu usage
3.460970291
max memory
1.7942528E8
stage attributes
key
value
output-size
5768
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 86 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 11 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: f_1(f_1(x, y), z) -> c_0 f_1(f_0(x, y), z) -> c_0 f_1(x, f_1(y, z)) -> f_1(f_0(x, y), z) f_1(x, f_1(y, z)) -> f_1(f_1(x, y), z) f_1(x, f_0(y, z)) -> f_1(f_1(x, y), z) f_1(x, f_0(y, z)) -> f_1(f_0(x, y), z) *top*_0(a_1) -> *top*_0(f_0(a_1, a_1)) f_0(a_1, x0) -> f_1(f_0(a_1, a_1), x0) f_0(x0, a_1) -> f_1(x0, f_0(a_1, a_1)) The replacement map contains the following entries: f_1: empty set c_0: empty set f_0: {1, 2} *top*_0: {1} a_1: empty set ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: f_1(f_1(x, y), z) -> c_0 f_1(f_0(x, y), z) -> c_0 f_1(x, f_1(y, z)) -> f_1(f_0(x, y), z) f_1(x, f_1(y, z)) -> f_1(f_1(x, y), z) f_1(x, f_0(y, z)) -> f_1(f_1(x, y), z) f_1(x, f_0(y, z)) -> f_1(f_0(x, y), z) *top*_0(a_1) -> *top*_0(f_0(a_1, a_1)) f_0(a_1, x0) -> f_1(f_0(a_1, a_1), x0) f_0(x0, a_1) -> f_1(x0, f_0(a_1, a_1)) The replacement map contains the following entries: f_1: empty set c_0: empty set f_0: {1, 2} *top*_0: {1} a_1: empty set Used ordering: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(f_1(x_1, x_2)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 + [[1, 0], [0, 0]] * x_2 >>> <<< POL(c_0) = [[0], [0]] >>> <<< POL(f_0(x_1, x_2)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 + [[1, 0], [1, 0]] * x_2 >>> <<< POL(*top*_0(x_1)) = [[0], [0]] + [[1, 1], [0, 0]] * x_1 >>> <<< POL(a_1) = [[0], [1]] >>> With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: *top*_0(a_1) -> *top*_0(f_0(a_1, a_1))
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