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TRS Conte Sensi 17651 pair #381733423
details
property
value
status
complete
benchmark
Ex1_Luc02b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n100.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.37562322617 seconds
cpu usage
3.130156811
max memory
2.03194368E8
stage attributes
key
value
output-size
7848
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRInnermostProof [EQUIVALENT, 0 ms] (2) CSR (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] (4) QCSDP (5) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QCSDP (8) QCSDPSubtermProof [EQUIVALENT, 19 ms] (9) QCSDP (10) PIsEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) QCSDP (13) QCSDPSubtermProof [EQUIVALENT, 0 ms] (14) QCSDP (15) PIsEmptyProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: from(X) -> cons(X, from(s(X))) first(0, Z) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) sel(0, cons(X, Z)) -> X sel(s(X), cons(Y, Z)) -> sel(X, Z) The replacement map contains the following entries: from: {1} cons: {1} s: {1} first: {1, 2} 0: empty set nil: empty set sel: {1, 2} ---------------------------------------- (1) CSRInnermostProof (EQUIVALENT) The CSR is orthogonal. By [CS_Inn] we can switch to innermost. ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: from(X) -> cons(X, from(s(X))) first(0, Z) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) sel(0, cons(X, Z)) -> X sel(s(X), cons(Y, Z)) -> sel(X, Z) The replacement map contains the following entries: from: {1} cons: {1} s: {1} first: {1, 2} 0: empty set nil: empty set sel: {1, 2} Innermost Strategy. ---------------------------------------- (3) CSDependencyPairsProof (EQUIVALENT) Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem. ---------------------------------------- (4) Obligation: Q-restricted context-sensitive dependency pair problem: The symbols in {from_1, s_1, first_2, sel_2, SEL_2, FROM_1, FIRST_2} are replacing on all positions. For all symbols f in {cons_2} we have mu(f) = {1}. The symbols in {U_1} are not replacing on any position. The ordinary context-sensitive dependency pairs DP_o are: SEL(s(X), cons(Y, Z)) -> SEL(X, Z)
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