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TRS Context Sensitive pair #516978727
details
property
value
status
complete
benchmark
Ex4_Zan97.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n173.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.02399516106 seconds
cpu usage
5.233062424
max memory
4.7706112E8
stage attributes
key
value
output-size
8950
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given CSR could be proven: (0) CSR (1) CSRInnermostProof [EQUIVALENT, 0 ms] (2) CSR (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] (4) QCSDP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, 0 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 (17) QCSDP (18) QCSDPSubtermProof [EQUIVALENT, 2 ms] (19) QCSDP (20) PIsEmptyProof [EQUIVALENT, 0 ms] (21) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: f(X) -> cons(X, f(g(X))) g(0) -> s(0) g(s(X)) -> s(s(g(X))) sel(0, cons(X, Y)) -> X sel(s(X), cons(Y, Z)) -> sel(X, Z) The replacement map contains the following entries: f: {1} cons: {1} g: {1} 0: empty set s: {1} 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: f(X) -> cons(X, f(g(X))) g(0) -> s(0) g(s(X)) -> s(s(g(X))) sel(0, cons(X, Y)) -> X sel(s(X), cons(Y, Z)) -> sel(X, Z) The replacement map contains the following entries: f: {1} cons: {1} g: {1} 0: empty set s: {1} 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 {f_1, g_1, s_1, sel_2, G_1, SEL_2, F_1} 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.
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