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TRS Contextsensitive pair #487092449
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
n149.star.cs.uiowa.edu
space
Transformed_outermost_08
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.46968 seconds
cpu usage
3.53429
user time
3.38331
system time
0.150981
max virtual memory
1.8472628E7
max residence set size
220588.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 63 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 3 ms] (4) CSR (5)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)) ---------------------------------------- (2) Obligation:
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