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TRS Contextsensitive pair #487092625
details
property
value
status
complete
benchmark
MYNAT_nosorts-noand-peanoSimple.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Maude_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.46399 seconds
cpu usage
3.21506
user time
3.06562
system time
0.149442
max virtual memory
1.8472628E7
max residence set size
216596.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 61 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5)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: U11(tt, M, N) -> U12(tt, M, N) U12(tt, M, N) -> s(plus(N, M)) plus(N, 0) -> N plus(N, s(M)) -> U11(tt, M, N) The replacement map contains the following entries: U11: {1} tt: empty set U12: {1} s: {1} plus: {1, 2} 0: empty set ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: U11(tt, M, N) -> U12(tt, M, N) U12(tt, M, N) -> s(plus(N, M)) plus(N, 0) -> N plus(N, s(M)) -> U11(tt, M, N) The replacement map contains the following entries: U11: {1} tt: empty set U12: {1} s: {1} plus: {1, 2} 0: empty set Used ordering: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(U11(x_1, x_2, x_3)) = [[1], [0]] + [[1, 0], [1, 1]] * x_1 + [[1, 1], [1, 1]] * x_2 + [[1, 1], [1, 1]] * x_3 >>> <<< POL(tt) = [[1], [1]] >>> <<< POL(U12(x_1, x_2, x_3)) = [[1], [0]] + [[1, 0], [1, 1]] * x_1 + [[1, 1], [1, 1]] * x_2 + [[1, 1], [1, 1]] * x_3 >>> <<< POL(s(x_1)) = [[0], [1]] + [[1, 0], [0, 1]] * x_1 >>> <<< POL(plus(x_1, x_2)) = [[1], [1]] + [[1, 1], [1, 1]] * x_1 + [[1, 1], [1, 1]] * x_2 >>> <<< POL(0) = [[0], [1]] >>> With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U12(tt, M, N) -> s(plus(N, M)) plus(N, 0) -> N ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules:
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