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TRS Context Sensitive pair #516978821
details
property
value
status
complete
benchmark
Ex3_3_25_Bor03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n001.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
1.96937990189 seconds
cpu usage
5.257490962
max memory
4.86674432E8
stage attributes
key
value
output-size
4960
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 91 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) CSRRRRProof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: app(nil, YS) -> YS app(cons(X, XS), YS) -> cons(X, app(XS, YS)) from(X) -> cons(X, from(s(X))) zWadr(nil, YS) -> nil zWadr(XS, nil) -> nil zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS)) prefix(L) -> cons(nil, zWadr(L, prefix(L))) The replacement map contains the following entries: app: {1, 2} nil: empty set cons: {1} from: {1} s: {1} zWadr: {1, 2} prefix: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: app(nil, YS) -> YS app(cons(X, XS), YS) -> cons(X, app(XS, YS)) from(X) -> cons(X, from(s(X))) zWadr(nil, YS) -> nil zWadr(XS, nil) -> nil zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS)) prefix(L) -> cons(nil, zWadr(L, prefix(L))) The replacement map contains the following entries: app: {1, 2} nil: empty set cons: {1} from: {1} s: {1} zWadr: {1, 2} prefix: {1} Used ordering: Polynomial interpretation [POLO]: POL(app(x_1, x_2)) = 2*x_1 + x_2 POL(cons(x_1, x_2)) = 2*x_1 POL(from(x_1)) = 1 + 2*x_1 POL(nil) = 0 POL(prefix(x_1)) = 1 + 2*x_1 POL(s(x_1)) = 1 + x_1 POL(zWadr(x_1, x_2)) = 2*x_1 + 2*x_2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: from(X) -> cons(X, from(s(X))) prefix(L) -> cons(nil, zWadr(L, prefix(L))) ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: app(nil, YS) -> YS app(cons(X, XS), YS) -> cons(X, app(XS, YS)) zWadr(nil, YS) -> nil
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