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TRS Context Sensitive pair #516978807
details
property
value
status
complete
benchmark
Ex15_Luc98.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n083.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
1.91070103645 seconds
cpu usage
4.835095387
max memory
4.70155264E8
stage attributes
key
value
output-size
3662
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 82 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: and(true, X) -> X and(false, Y) -> false if(true, X, Y) -> X if(false, X, Y) -> Y add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) from(X) -> cons(X, from(s(X))) The replacement map contains the following entries: and: {1} true: empty set false: empty set if: {1} add: {1} 0: empty set s: empty set first: {1, 2} nil: empty set cons: empty set from: empty set ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: and(true, X) -> X and(false, Y) -> false if(true, X, Y) -> X if(false, X, Y) -> Y add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) from(X) -> cons(X, from(s(X))) The replacement map contains the following entries: and: {1} true: empty set false: empty set if: {1} add: {1} 0: empty set s: empty set first: {1, 2} nil: empty set cons: empty set from: empty set Used ordering: Polynomial interpretation [POLO]: POL(0) = 2 POL(add(x_1, x_2)) = 2*x_1 + 2*x_2 POL(and(x_1, x_2)) = 2 + x_1 + x_2 POL(cons(x_1, x_2)) = 0 POL(false) = 2 POL(first(x_1, x_2)) = 2 + 2*x_1 + x_2 POL(from(x_1)) = 0 POL(if(x_1, x_2, x_3)) = x_1 + x_2 + x_3 POL(nil) = 2 POL(s(x_1)) = 2 POL(true) = 2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: and(true, X) -> X and(false, Y) -> false
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