/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- NO proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given CSR could be disproven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 96 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 10 ms] (4) CSR (5) ContextSensitiveLoopProof [COMPLETE, 0 ms] (6) NO ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: zeros -> cons(0, zeros) U11(tt, L) -> U12(tt, L) U12(tt, L) -> s(length(L)) U21(tt, IL, M, N) -> U22(tt, IL, M, N) U22(tt, IL, M, N) -> U23(tt, IL, M, N) U23(tt, IL, M, N) -> cons(N, take(M, IL)) length(nil) -> 0 length(cons(N, L)) -> U11(tt, L) take(0, IL) -> nil take(s(M), cons(N, IL)) -> U21(tt, IL, M, N) The replacement map contains the following entries: zeros: empty set cons: {1} 0: empty set U11: {1} tt: empty set U12: {1} s: {1} length: {1} U21: {1} U22: {1} U23: {1} take: {1, 2} nil: empty set ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: zeros -> cons(0, zeros) U11(tt, L) -> U12(tt, L) U12(tt, L) -> s(length(L)) U21(tt, IL, M, N) -> U22(tt, IL, M, N) U22(tt, IL, M, N) -> U23(tt, IL, M, N) U23(tt, IL, M, N) -> cons(N, take(M, IL)) length(nil) -> 0 length(cons(N, L)) -> U11(tt, L) take(0, IL) -> nil take(s(M), cons(N, IL)) -> U21(tt, IL, M, N) The replacement map contains the following entries: zeros: empty set cons: {1} 0: empty set U11: {1} tt: empty set U12: {1} s: {1} length: {1} U21: {1} U22: {1} U23: {1} take: {1, 2} nil: empty set Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(U11(x_1, x_2)) = x_1 + x_2 POL(U12(x_1, x_2)) = x_1 + x_2 POL(U21(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(U22(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(U23(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(cons(x_1, x_2)) = x_1 + x_2 POL(length(x_1)) = 1 + x_1 POL(nil) = 1 POL(s(x_1)) = x_1 POL(take(x_1, x_2)) = 1 + x_1 + x_2 POL(tt) = 1 POL(zeros) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: length(nil) -> 0 ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: zeros -> cons(0, zeros) U11(tt, L) -> U12(tt, L) U12(tt, L) -> s(length(L)) U21(tt, IL, M, N) -> U22(tt, IL, M, N) U22(tt, IL, M, N) -> U23(tt, IL, M, N) U23(tt, IL, M, N) -> cons(N, take(M, IL)) length(cons(N, L)) -> U11(tt, L) take(0, IL) -> nil take(s(M), cons(N, IL)) -> U21(tt, IL, M, N) The replacement map contains the following entries: zeros: empty set cons: {1} 0: empty set U11: {1} tt: empty set U12: {1} s: {1} length: {1} U21: {1} U22: {1} U23: {1} take: {1, 2} nil: empty set ---------------------------------------- (3) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: zeros -> cons(0, zeros) U11(tt, L) -> U12(tt, L) U12(tt, L) -> s(length(L)) U21(tt, IL, M, N) -> U22(tt, IL, M, N) U22(tt, IL, M, N) -> U23(tt, IL, M, N) U23(tt, IL, M, N) -> cons(N, take(M, IL)) length(cons(N, L)) -> U11(tt, L) take(0, IL) -> nil take(s(M), cons(N, IL)) -> U21(tt, IL, M, N) The replacement map contains the following entries: zeros: empty set cons: {1} 0: empty set U11: {1} tt: empty set U12: {1} s: {1} length: {1} U21: {1} U22: {1} U23: {1} take: {1, 2} nil: empty set Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(U11(x_1, x_2)) = x_1 + x_2 POL(U12(x_1, x_2)) = x_1 + x_2 POL(U21(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + x_4 POL(U22(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + x_4 POL(U23(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + x_4 POL(cons(x_1, x_2)) = x_1 + x_2 POL(length(x_1)) = x_1 POL(nil) = 0 POL(s(x_1)) = x_1 POL(take(x_1, x_2)) = 1 + x_1 + x_2 POL(tt) = 0 POL(zeros) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: take(0, IL) -> nil ---------------------------------------- (4) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: zeros -> cons(0, zeros) U11(tt, L) -> U12(tt, L) U12(tt, L) -> s(length(L)) U21(tt, IL, M, N) -> U22(tt, IL, M, N) U22(tt, IL, M, N) -> U23(tt, IL, M, N) U23(tt, IL, M, N) -> cons(N, take(M, IL)) length(cons(N, L)) -> U11(tt, L) take(s(M), cons(N, IL)) -> U21(tt, IL, M, N) The replacement map contains the following entries: zeros: empty set cons: {1} 0: empty set U11: {1} tt: empty set U12: {1} s: {1} length: {1} U21: {1} U22: {1} U23: {1} take: {1, 2} ---------------------------------------- (5) ContextSensitiveLoopProof (COMPLETE) zeros -> cons(0, zeros) U11(tt, L) -> U12(tt, L) U12(tt, L) -> s(length(L)) U21(tt, IL, M, N) -> U22(tt, IL, M, N) U22(tt, IL, M, N) -> U23(tt, IL, M, N) U23(tt, IL, M, N) -> cons(N, take(M, IL)) length(cons(N, L)) -> U11(tt, L) take(s(M), cons(N, IL)) -> U21(tt, IL, M, N) ---------- Loop: ---------- U12(tt, zeros) -> s(length(zeros)) with rule U12(tt, L) -> s(length(L)) at position [] and matcher [L / zeros] s(length(zeros)) -> s(length(cons(0, zeros))) with rule zeros -> cons(0, zeros) at position [0,0] and matcher [ ] s(length(cons(0, zeros))) -> s(U11(tt, zeros)) with rule length(cons(N, L)) -> U11(tt, L) at position [0] and matcher [N / 0, L / zeros] s(U11(tt, zeros)) -> s(U12(tt, zeros)) with rule U11(tt, L) -> U12(tt, L) at position [0] and matcher [L / zeros] Now an instance of the first term with Matcher [ ] occurs in the last term at position [0]. Context: s([]) We used [[THIEMANN_LOOPS_UNDER_STRATEGIES], Theorem 1] to show that this loop is an context-sensitive loop. ---------------------------------------- (6) NO